Trying to escape his pursuers, a secret agent skis off a slope inclined at 30° below the horizontal at 55 km/h. to survive and land on the snow 100 m below, he must clear a gorge 43 m wide. does he make it? ignore air resistance.

Answers

Answer 1

The agent made it since the range of his motion is greater than the width of the gorge.

The given parameters;

inclination of the slope, Ф = 30°velocity of the agent, v = 55 km/h vertical distance below the snow, h = 100 mwidth of the gorge the agent must cross, w = 43 m

Assume downward motion to be negative.

The initial vertical component of the velocity in m/s;

[tex]v_0_y = v_0 \times sin(30)\\\\v_o_y = - 55 \ km/h \times sin(30) = -27.5 \ km/h = -7.64 \ m/s[/tex]

Determine the final vertical velocity of the agent;

[tex]v_y_f^2 = v_0_y^2 - 2gh\\\\v_y_f^2 = (-7.64)^2 - 2(9.8)(-100)\\\\v_y_f^2 = 2018.37\\\\v_y_f = \sqrt{2018.37} \\\\v_y_f = -44.93 \ m/s[/tex]

Determine the time of motion;

[tex]v_y_f = v_0y - gt\\\\-44.93 = -7.64 - 9.8t\\\\9.8t = 44.93 - 7.64\\\\9.8t = 37.29\\\\t = \frac{37.29}{9.8} = 3.81 \ s[/tex]

Determine the horizontal component of the initial velocity;

[tex]v_0_x = v_0 \times cos(\theta)\\\\v_0_x = 55 \ km/h \times cos(30) = 47.63 \ km/h = 13.2 \ m/s[/tex]

Determine the range of the of the agent's motion;

[tex]X = v_0_x \times t\\\\X = 13.2\ m/s \times 3.81 \ s\\\\X = 50.3 \ m[/tex]

Thus, the agent made it since the range of his motion is greater than the width of the gorge.

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Answer 2
Final answer:

Using the principles of projectile motion, we can determine that the secret agent will be able to clear the gorge and make it safely across. The agent's horizontal distance covered is 76.09 m, which is greater than the width of the gorge (43 m).

Explanation:

To determine if the secret agent can make it across the gorge, we need to analyze his motion using the principles of projectile motion. Since the slope is inclined at 30° below the horizontal, we can break down the velocity into horizontal and vertical components. The horizontal component remains constant, while the vertical component changes due to the acceleration due to gravity. We can use the kinematic equations to determine the time it takes for the agent to reach the other side of the gorge. If the time is less than the time it takes for the agent to fall vertically, then he will clear the gorge and land safely on the snow.

Given that the agent skis off the slope at a speed of 55 km/h, we first need to convert this to m/s. 55 km/h is equal to 15.28 m/s. The horizontal component of the velocity remains constant at 15.28 m/s. We can determine the vertical component by multiplying the speed by the sine of the angle (30°). The vertical component is therefore 7.64 m/s. Using the equation d = v*t + 0.5*a*t^2, we can solve for time using the vertical component and the vertical distance of 100 m. Plugging in the values, we get:

100 = 7.64*t + 0.5*(-9.8)*t^2

This equation simplifies to:

4.9*t^2 + 7.64*t - 100 = 0

Solving for t, we find two possible values, t = -4.22 s and t = 4.98 s. Since time cannot be negative, we discard the negative value, leaving us with t = 4.98 s. Now we need to determine the horizontal distance the agent will travel during this time. We can use the equation d = v*t, plugging in the horizontal velocity and time:

d = 15.28 m/s * 4.98 s = 76.09 m

The horizontal distance covered by the agent is 76.09 m. Since the gorge is 43 m wide, the agent will be able to clear the gorge and make it across safely. Therefore, the secret agent does make it across the gorge.


Related Questions

At what point or points on the x-axis is the electric potential zero a +3.0 nc charge is at x=0 cm and a -1.0nc charge is at x=4cm.

Answers

Answer:

Potential will be zero at two points

x = 3 cm

x = 6 cm

Explanation:

Let the first point at which potential is zero is lying between two charges

so we will have

[tex]\frac{kq_1}{x} = \frac{kq_2}{L - x}[/tex]

[tex]\frac{3nC}{x} = \frac{1nC}{4 - x}[/tex]

[tex]3(4 - x) = x[/tex]

[tex]x = 3 cm[/tex]

Let another point lies on the right side of -1 nC on x axis

so we will have

[tex]\frac{kq_1}{x} = \frac{kq_2}{x-4}[/tex]

[tex]\frac{3}{x} = \frac{1}{x-4}[/tex]

[tex]3(x - 4) = x[/tex]

[tex]x = 6 cm[/tex]

The points on x - axis in which the electric potential between the two charges is zero are 3 cm and 6 cm.

The given parameters;

q₁ = 3 nC

q₂ = -1 nC

Let the point in which the potential between the two charges equal zero, lie  between the two charges.

Let the point = x₁

         (+q₁)----------------------(x₁)------------------------(-q₂)

The electric potential of due to each charge is calculated as;

[tex]\frac{kq_1}{x_1} = \frac{kq_2}{4-x_1}[/tex]

[tex]\frac{3k}{x_1} = \frac{k}{4-x_1}\\\\3k(4-x_1) = kx_1\\\\3(4-x_1) = x_1\\\\12 - 3x_1 = x_1\\\\4x_1 = 12\\\\x_1 = \frac{12}{4} \\\\x_1 = 3 \ cm[/tex]

Since the second charge is negative, another point in which the potential between the two charges will be zero will be right of second charge;

          (+q₁)----------------------------(-q₂)------------------(x₂)

[tex]\frac{kq_1}{x_2} = \frac{kq_2}{x_2 - 4} \\\\\frac{3k}{x_2} = \frac{k}{x_2 - 4} \\\\3(x_2-4) = x_2\\\\3x_2 - 12 = x_2\\\\2x_2 = 12\\\\x_2 = \frac{12}{2} \\\\x_2 = 6 \ cm[/tex]

Thus, the points on x - axis in which the electric potential between the two charges is zero are 3 cm and 6 cm.

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How many categories of hurricanes are there

Answers

There are 5 categories of hurricanes.

I don't know the 5 categories but i know there are 5

~Jax

What elements compose the stars and planets in the universe

Answers

27% helium and 71% hydrogen

________ is a phenomenon of nature that has been proven to invariably occur whenever certain conditions exist.

Answers

Scientific law...is a phenomenon of nature that has been proven to invariably occur whenever a certain conditions exist

Answer:

Scientific law

Explanation:

In general, a scientific law is the description of an observed phenomenon, that is, it represents a phenomenon of nature that has proven invariably to occur whenever certain conditions exist. However, scientific law does not explain why the phenomenon exists or causes it. The explanation of the phenomenon is called scientific theory. Theories become laws after scientific research.

A transformer has 1400 turns on the primary and 110 on the secondary.?If the primary is connected to a 120V outlet and draws 3.0x10^-2 Amps, what are the voltage and current of the secondary? A) 1500 V, 2.4x10^-3 A B) 1500 V, 0.38 A C) 9.4 V, 2.4x10^-3 A D) 9.4 V, 0.38 A

Answers

Answer:

D) 9.4 V, 0.38 A

1) Voltage in the secondary coil: 9.4 V

The transformer equation states that:

[tex]\frac{V_p}{N_p}=\frac{V_s}{N_s}[/tex]

where

Vp = 120 V is the voltage in the primary coil

Np = 1400 is the number of turns in the primary coil

Vs = ? is the voltage in the secondary coil

Ns = 110 is the number of turns in the secondary coil

Solving the formula for Vs, we find

[tex]V_s = N_s \frac{V_p}{N_p}=(110)\frac{120 V}{1400}=9.4 V[/tex]

2) Current in the secondary coil: 0.38 A

A transformer is considered to be 100% efficient: it means that there is no loss of power, so the power in input is equal to the power in output

[tex]P_i = P_o\\V_p I_p = V_s I_s[/tex]

where

Vp = 120 V is the voltage in the primary coil

[tex]I_p = 3.0\cdot 10^{-2} A[/tex] is the current in the primary coil

Vs = 9.4 V is the voltage in the secondary coil

[tex]I_s[/tex] is the current in the secondary coil

Solving the equation for [tex]I_s[/tex],

[tex]I_s = \frac{V_p I_p}{V_s}=\frac{(120 V)(3.0\cdot 10^{-2}A)}{9.4 V}=0.38 A[/tex]

Suppose you have two capacitors and want to use them to store the maximum amount of energy by connecting them across a voltage source. You should connect them

Answers

Answer:

Connect them in parallel

Explanation:

The energy stored by two capacitors connected to the same voltage source is given by

[tex]U=\frac{1}{2}C_T V^2[/tex]

where

[tex]C_T[/tex] is the total capacitance of the two capacitors

V is the voltage of the source

In order to maximize the energy stored U, we need to maximize [tex]C_T[/tex]. We have:

- In parallel, the total capacitance is given by the sum of the individual capacitances:

[tex]C_T(p) = C_1 + C_2[/tex]

- In series, the total capacitance is given by:

[tex]C_T(s)=\frac{1}{\frac{1}{C_1}+\frac{1}{C_2}}[/tex]

Comparing the two equations, we notice that [tex]C_T(p)>C_T(s)[/tex], so the parallel configuration is the one that maximizes the energy stored.

Final answer:

To store the maximum amount of energy, capacitors should be connected in parallel as this configuration allows each capacitor to experience the same voltage as the source, maximizing the total stored charge and energy.

Explanation:

If you wish to store the maximum amount of energy in capacitors when connecting them across a voltage source, you should connect them in parallel. In a parallel configuration, each capacitor experiences the same voltage as the source. This setup ensures that the total capacitance is the sum of the individual capacitances, thus allowing for the storage of a maximum amount of energy. Capacitors in parallel have the advantage of maintaining the voltage across each capacitor equal to the source voltage, leading to a higher total charge stored in the system. Conversely, capacitors in series have a reduced total capacitance, as the voltage divides among them, making parallel connection the better choice for maximizing energy storage.

Eight different values of resistance can be obtained by connecting together three resistors 6.50 Ω, 7.60 Ω, and 1.70 Ω in all possible ways. What are the values in the following situations? All the resistors are connected in series. Ω All the resistors are connected in parallel. Ω The 6.50 Ω and 7.60 Ω resistors are connected in parallel, and the 1.70-Ω resistor is connected in series with the parallel combination. Ω The 6.50 Ω and 1.70 Ω resistors are connected in parallel, and the 7.60-Ω resistor is connected in series with the parallel combination. Ω The 7.60 Ω and 1.70 Ω resistors are connected in parallel, and the 6.50-Ω resistor is connected in series with the parallel combination. Ω The 6.50 Ω and 7.60 Ω resistors are connected in series, and the 1.70-Ω resistor is connected in parallel with the series combination. Ω The 6.50 Ω and 1.70 Ω resistors are connected in series, and the 7.60-Ω resistor is connected in parallel with the series combination. Ω The 7.60 Ω and 1.70 Ω resistors are connected in series, and the 6.50-Ω resistor is connected in parallel with the series combination. Ω Additional Materials

Answers

Final answer:

The resistance when all three resistors are connected in series is 15.80 Ω. The resistance when all three resistors are connected in parallel is 1.67 Ω. For the other combinations, the same principles of series and parallel connections can be applied to calculate the resistances.

Explanation:

In a series circuit, the resistors are connected end-to-end, such that the total resistance is the sum of the individual resistances. So, in this case, the resistance when all three resistors are connected in series would be 6.50 Ω + 7.60 Ω + 1.70 Ω = 15.80 Ω.

In a parallel circuit, the resistors are connected in branches, such that the total resistance is determined by the reciprocal of the sum of the reciprocals of the individual resistances. So, in this case, the resistance when all three resistors are connected in parallel would be 1/(1/6.50 Ω + 1/7.60 Ω + 1/1.70 Ω) = 1.67 Ω.

For the other combinations, you can apply the same principles of series and parallel connections to calculate the resistances.

A bullet of mass 0.016 kg traveling horizontally at a speed of 280 m/s embeds itself in a block of mass 3 kg that is sitting at rest on a nearly frictionless surface. (a) What is the speed of the block after the bullet embeds itself in the block? vf= m/s (b) Calculate the total translational kinetic energy before and after the collision. Ktrans, i= J Ktrans, f= J (c) Compare the two results and explain why there is a difference. The internal energy of the block-bullet system has increased. The Energy Principle isn't valid for an inelastic collision. Some of the momentum is lost in an inelastic collision.

Answers

(a) 1.49 m/s

The conservation of momentum states that the total initial momentum is equal to the total final momentum:

[tex]p_i = p_f\\m u_b + M u_B = (m+M)v[/tex]

where

m = 0.016 kg is the mass of the bullet

[tex]u_b = 280 m/s[/tex] is the initial velocity of the bullet

M = 3 kg is the mass of the block

[tex]u_B = 0[/tex] is the initial velocity of the block

v = ? is the final velocity of the block and the bullet

Solving the equation for v, we find

[tex]v=\frac{m u_b}{m+M}=\frac{(0.016 kg)(280 m/s)}{0.016 kg+3 kg}=1.49 m/s[/tex]

(b) Before: 627.2 J, after: 3.3 J

The initial kinetic energy is (it is just the one of the bullet, since the block is at rest):

[tex]K_i = \frac{1}{2}mu_b^2 = \frac{1}{2}(0.016 kg)(280 m/s)^2=627.2 J[/tex]

The final kinetic energy is the kinetic energy of the bullet+block system after the collision:

[tex]K_f = \frac{1}{2}(m+M)v^2=\frac{1}{2}(0.016 kg+3 kg)(1.49 m/s)^2=3.3 J[/tex]

(c) The Energy Principle isn't valid for an inelastic collision.

In fact, during an inelastic collision, the total momentum of the system is conserved, while the total kinetic energy is not: this means that part of the kinetic energy of the system is losted in the collision. The principle of conservation of energy, however, is still valid: in fact, the energy has not been simply lost, but it has been converted into other forms of energy (thermal energy).

(a) The final speed of the block after the collision is 1.485 m/s.

(b) The kinetic energy before the collision is 627.2 J and The total kinetic energy of the system after the collision is 3.33 J.

(c) The difference in the two kinetic energy is due to energy lost to frictional force during the collision.

Final speed of the block

The final speed of the block after the collision is determined by applying principle of conservation of linear momentum.

m₁u₁ + m₂u₂ = v(m₁+ m₂)

0.016(280) + 3(0) = v(0.016 + 3)

4.48 = 3.016v

v = 4.48/3.016

v = 1.485 m/s

Total Kinetic energy before and after collision

The kinetic energy before the collision is calculated as follows;

K.E i = ¹/₂mv²

K.Ei = 0.5 x 0.016 x 280²

K.Ei = 627.2 J

The total kinetic energy of the system after the collision is calculated as follows;

K.Ef = ¹/₂(m1 + m2) v²

K.Ef = ¹/₂(0.016 + 3) 1.485²

K.Ef = 3.33 J

The difference in the two kinetic energy is due to energy lost to frictional force during the collision.

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ANSWER TRUE OR FALSE: The people in the northern hemisphere experience the seasons opposite of the people in the southern hemisphere

Answers

That's TRUE.

For example:

--  When it's Winter in Canada, the USA, and France, it's Summer in Australia, Paraguay, and Namibia.  (This is the end of December, all of January and February, and most of March.)

-- When it's Winter in Tasmania, South Africa, and Botswana, it's Summer in Germany, Israel, and Mexico.  (This is the end of June, all of July and August, and most of September.)

-- The Spring and Fall are opposite too.

Answer: true

Explanation:

The strength of the Earth’s magnetic field B at the equator is approximately equal to 5 × 10−5 T. The force on a charge q moving in a direction perpendicular to a magnetic field is given by F = q v B, where v is the speed of the particle. The direction of the force is given by the right-hand rule. Suppose you rub a balloon in your hair and your head acquires a static charge of 6 × 10−9 C. If you are at the equator and driving west at a speed of 80 m/s, what is the strength of the magnetic force on your head due to the Earth’s magnetic field? Answer in units of N.

Answers

Answer:

[tex]2.4\cdot 10^{-11} N[/tex]

Explanation:

Since the Earth's magnetic field is perpendicular to your direction of motion, the strength of the magnetic force exerted on your head is given by:

[tex]F=qvB[/tex]

where:

[tex]q=6\cdot 10^{-9}C[/tex] is the charge on your head

[tex]v=80 m/s[/tex] is the speed at which you are moving

[tex]B=5\cdot 10^{-5} T[/tex] is the strength of the magnetic field of the Earth

By substituting these numbers into the equation, we find the strength of the magnetic force:

[tex]F=(6\cdot 10^{-9}C)(80 m/s)(5\cdot 10^{-5} T)=2.4\cdot 10^{-11} N[/tex]

When electric current is flowing in a metal, the electrons are moving.A. at nearly the speed of lightB. at the speed of lightC. at the speed of sound in the metalD. at the speed of sound in airE. at none of the above speeds

Answers

I believe its E.

Traveling through metal, electrons can not go the speed of light

Answer:

E. at none of the above speeds

Explanation:

When current flowing through the metal then the speed of electrons in metal is not very high.

This speed of all electrons inside metal is opposite the the electric field which is due to the applied potential difference on the metal by external battery.

As we know that

[tex]\Delta V = i R[/tex]

here for the current flowing in the metal the all the free electrons will move at drift speed which is given as

[tex]i = neAv_d[/tex]

here speed of electrons will be

[tex]v_d[/tex] = drift speed

n = number density of electrons

A = crossectional area

e = charge of an electron

in general this speed is very small and approximately of order cm/s

The first stage in designing your presentation is to make a list of questions that will enable you to research the topic.

Your presentation should answer these questions: Where is the magnet that causes Earth’s magnetic field? What is this magnet made of?

What is the solar wind? What happens when Earth’s magnetic field interacts with the solar wind?

Does Earth’s magnetic field protect the planet?

What are the Van Allen belts, and how are they related to Earth’s magnetic field?

What are auroras, and how are they related to Earth’s magnetic field?

How does the principle of electromagnetism explain the interaction between Earth’s magnetic field and the solar wind? Write down two additional questions about Earth’s magnetic field that will make your presentation more informative.

Answers

The Earth's magnetic field is believed to be generated by electric currents in the conductive iron alloys of its core, created by convection currents due to heat escaping from the core.

The solar wind is a stream of charged particles released from the upper atmosphere of the Sun, called the corona. This plasma consists of mostly electrons, protons and alpha particles with kinetic energy between 0.5 and 10 keV. Embedded within the solar-wind plasma is the interplanetary magnetic field. As Earth cruises through the black sea of space at about 67,000 mph (108,000 km/h), the planet's magnetic field pushes aside solar wind — the constant stream of plasma particles ejected by the sun — the same way the bow of a speeding motorboat pushes aside water.

The Earth's magnetic field serves to deflect most of the solar wind, whose charged particles would otherwise strip away the ozone layer that protects the Earth from harmful ultraviolet radiation.

A Van Allen radiation belt is a zone of energetic charged particles, most of which originate from the solar wind, that are captured by and held around a planet by that planet's magnetic field. Earth has two such belts and sometimes others may be temporarily created. 

An aurora (plural: auroras or aurorae), sometimes referred to as polar lights, northern lights (auroraborealis), southern lights (aurora australis), is a natural light display in the Earth's sky, predominantly seen in the high-latitude regions (around the Arctic and Antarctic). Charged particles from the sun strike atoms in Earth's atmosphere, they cause electrons in the atoms to move to a higher-energy state. When the electrons drop back to a lower energy state, they release a photon: light. This process creates the beautiful aurora, or northern lights.

Simulation of the interaction between Earth's magnetic field and the interplanetary magnetic field. Earth is largely protected from the solar wind, a stream of energetic charged particles emanating from the Sun, by its magnetic field, which deflects most of the charged particles.

What causes an aurora?

What does Earth do to the planet's magnetic fieldpushes aside solar wind?

Final answer:

Earth's magnetic field is created by the movement of molten iron within the Earth's outer core. This field protects the planet from the solar wind. Solar wind's interactions with the field create phenomena like the Van Allen belts and auroras.

Explanation:

The magnet that causes Earth’s magnetic field is not a physical magnet but rather the movement of molten iron within the Earth's outer core. This movement generates electric currents which, in turn, create a magnetic field.

Solar wind

is a stream of charged particles released from the Sun's atmosphere and when it hits the Earth’s magnetic field, it gets diverted causing a bow shock.

Yes, Earth’s magnetic field does protect the planet from the solar wind by acting as a shield that deflects the solar radiation around the planet. The Van Allen belts are zones of energized particles, trapped by Earth's magnetic field, and are essentially an extension of Earth's magnetic field into space. Aurora Borealis (Northern Lights) and Aurora Australis (Southern Lights), collectively called auroras, are caused by the interaction of the solar wind with Earth's magnetic field causing charged particles to emit light.

The principle of electromagnetism explains this interaction, as the charged particles from the solar wind have electric fields associated with them, which experience a force in Earth's magnetic field, causing them to move along the field lines. The additional questions can include: How does Earth’s magnetic field affect navigation? What are the impacts of the magnetic field flipping?

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The color of light most readily absorbed by water is _________.

Answers

answer is the color white

A piano string sounds a middle A by vibrating primarily at 220 Hz.a)Calculate its period.b)Calculate its angular frequency.c)Calculate the period for a soprano singing a "high A," two octaves up, which is four times the frequency of the piano string.d)Calculate the angular frequency for a soprano singing a "high A," two octaves up, which is four times the frequency of the piano string.

Answers

Final answer:

The period and angular frequency of a piano string playing a middle A and a soprano singing a high A are calculated using the given frequencies.

Explanation:

a) To calculate the period of a wave, we can use the formula: period = 1/frequency. In this case, the frequency is 220 Hz. Therefore, the period is 1/220 s, which is approximately 0.0045 s.

b) The angular frequency, represented by the symbol ω, is equal to 2π times the frequency. So, for the piano string with a frequency of 220 Hz, the angular frequency is 2π * 220 rad/s.

c) For a soprano singing a high A two octaves up, which has a frequency four times that of the piano string, the period would be 1/ (4 * 220) s.

d) Finally, to calculate the angular frequency for the soprano singing a high A two octaves up, we multiply the frequency by 2π. Therefore, the angular frequency is 2π * (4 * 220) rad/s.

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50 POINTS! A supplier wants to make a profit by buying metal by weight at one altitude and selling it at the same price per pound weight at another altitude. The supplier should
a. buy at high altitude and sell at low altitude
b. buy at low altitude and sell at high altitude
c. disregard altitude because it makes no difference

Answers

Choice A is the right answer! Buy at high altitude and sell at low altitude

Hope this helps :)

They should A- buy at a high altitude and sell at a low altitude

Determine the stopping distances for an automobile with an initial speed of 95 km/h and human reaction time of 1.0 s : (a) for an acceleration a = -5.5 m/s2 : (b) for a = -6.6 m/s2

Answers

Final answer:

To determine the stopping distances for an automobile with different accelerations, we can calculate the distance traveled during the human reaction time and the deceleration distance. By adding these two distances, we can find the total stopping distance for each acceleration.

Explanation:

The stopping distance of an automobile can be determined by calculating the distance traveled during the human reaction time and the distance traveled during the deceleration period.

(a) For an acceleration of -5.5 m/s², the human reaction time is 1.0 s.

The distance traveled during the reaction time can be calculated using the formula: distance = initial velocity * reaction time. In this case, the initial velocity is 95 km/h, which needs to be converted to m/s.

The deceleration distance can be calculated using the formula: distance = (initial velocity²)/(2 * acceleration).

The stopping distance can be found by adding the distance traveled during the reaction time and the deceleration distance.

(b) The same process can be applied for an acceleration of -6.6 m/s².

A 44.0-kg child takes a ride on a Ferris wheel that rotates four times each minute and has a diameter of 20.0 m.

(a) What is the centripetal acceleration of the child?
(b) What force (magnitude and direction) does the seat exert on the child at the lowest point of the ride?
(c) What force does the seat exert on the child at the highest point of the ride?
(d) What force does the seat exert on the child when the child is halfway between the top and bottom? (Assume the Ferris wheel is rotating clockwise and the child is moving upward.)

Answers

(a) 1.76 m/s^2

The centripetal acceleration of the child is given by:

[tex]a_c=\omega^2 r[/tex]

where

[tex]\omega[/tex] is the angular velocity

r is the radius of the wheel

The radius of the wheel is half the diameter:

[tex]r=\frac{d}{2}=\frac{20.0 m}{2}=10.0 m[/tex]

The wheel makes 4 revolution per minute, so the angular velocity is

[tex]\omega=4 rev/min[/tex]

Let's remind that

[tex]1 rev = 2 \pi rad[/tex]

[tex]1 min = 60 s[/tex]

So the angular velocity is

[tex]\omega=(4 rev/min) \cdot \frac{2 \pi rad/rev}{60 s/min}=0.42 rad/s[/tex]

So, the centripetal acceleration is

[tex]a_c=(0.42 rad/s)^2(10.0 m)=1.76 m/s^2[/tex]

(b) 509.1 N, upward

At the lowest point of the ride, we have the following forces:

- Normal force exerted by the seat on the child: N, upward

- Weight of the child: W = mg, downward

The resultant of these forces must be equal to the centripetal force, which is upward (towards the centre of the wheel), so we have the following equation

[tex]N-mg = ma_c[/tex]

From which we can find the normal reaction of the seat on the child:

[tex]N=m(g+a_c)=(44.0 kg)(9.81 m/s^2+1.76 m/s^2)=509.1 N[/tex]

(c) 354.2 N, upward

At the highest point of the ride, we have the following forces:

- Normal force exerted by the seat on the child: N, upward

- Weight of the child: W = mg, downward

The resultant of these forces must be equal to the centripetal force, which this time is downward (towards the centre of the wheel), so we have the following equation

[tex]mg-N = ma_c[/tex]

From which we can find the normal reaction of the seat on the child:

[tex]N=m(g-a_c)=(44.0 kg)(9.81 m/s^2-1.76 m/s^2)=354.2 N[/tex]

(d) 431.6 N, upward

When the child is halfway between the top and the bottom, the normal force exerted by the seat on the child is simply equal to the weight of the child; therefore we have:

[tex]N=mg=(44.0 kg)(9.81 m/s^2)=431.6 N[/tex]

Centripetal acceleration is towards the center. The force seat exerts on the child when the child is halfway between the top and bottom is 431.64 N.

What is centripetal acceleration?

The centripetal acceleration is caused due to change in direction of the body which is in a circular motion, the acceleration is towards the center of the circle. It is calculated using the formula,

[tex]a = \dfrac{v^2}{r}[/tex]

Given to us

Mass of the child, m = 44 kg

The angular velocity of the wheel, ω = 4 rev/ min. = 0.42 rev\sec

Diameter of the wheel, d = 20.0 m

The radius of the wheel, r = 10.0 m

A.) The centripetal acceleration of the child can be given as,

[tex]a = \dfrac{v^2}{r}[/tex]

Also, we know that the linear velocity is written as,

[tex]v = \omega \times r[/tex]

Substitute the value,

[tex]a = \dfrac{(\omega r)^2}{r} = \omega^2 r[/tex]

[tex]a = (0.42)^2 \times 10 = 1.764\ m/s^2[/tex]

B.) Force that the seat experts on the child,

At the point when the child is at the lowest point of the wheel,

there are three forces that will work on the child,

The normal force, that will act upwards on the child, N

The weight of the child that will act downwards, W = mg

The centripetal force that will act toward the center therefore upwards, [tex]F_c = m a[/tex]

Taking all the vertical forces,

[tex]\sum F_y = 0\\\\N + F_c = W\\\\N + ma = mg\\\\N = mg-ma\\\\N=m(g-a)\\\\\text{Substitute the values}\\\\N = 44(9.81-1.76)\\\\N = 354.2\ N[/tex]

C.) Force that the seat experts on the child,

At the point when the child is at the highest point of the wheel,

there are three forces that will work on the child,

The normal force, that will act upwards on the child, N

The weight of the child that will act downwards, W = mg

The centripetal force that will act toward the center therefore downwards, [tex]F_c = m a[/tex]

Taking all the vertical forces,

[tex]\sum F_y = 0\\\\N = F_c + W\\\\N = ma + mg\\\\N = mg+ma\\\\N=m(g+a)\\\\\text{Substitute the values}\\\\N = 44(9.81+1.76)\\\\N = 509.08\ N[/tex]

D.)C.) Force that the seat experts on the child,

At the point when the child is at the midway of the wheel,

there are three forces that will work on the child,

The normal force, that will act upwards on the child, N

The weight of the child that will act downwards, W = mg

The centripetal force that will act toward the center therefore Rightside, [tex]F_c = m a[/tex]

Taking all the vertical forces,

[tex]\sum F_y = 0\\\\N = W\\\\N = mg\\\\\text{Substitute the values}\\\\N = 44\times 9.81\\\\N = 431.64\ N[/tex]

Hence, the force seat exerts on the child when the child is halfway between the top and bottom is 431.64 N.

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Waste disposals cost less than recycling. true or false

Answers

True.

Recycling programs in the United States have now become a major component  in today's waste management, unfortunately, recycling programs are not cost effective and are also considered to be one of most expensive ways of ridding waste.  According to author Harvey Black of the Environmental Health Perspectives Journal, in San Jose, California “it costs $28 per ton to landfill waste compared with $147 a ton to recycle” (Black 1006).

Large electric fields in cell membranes cause ions to move through the cell wall. The field strength in a typical membrane is 1.0 x 10 7 N/C. What is the magnitude of the force on a calcium ion with charge +e? What is its acceleration?Is it possible for a particle with the same charge as as calcium to have a different acceleration if placed at this location?What would change the acceleration: mass of the particle? diameter of the particle?

Answers

1) Magnitude of the force: [tex]1.6\cdot 10^{-12} N[/tex]

The magnitude of the electric force on an electric charge is:

[tex]F=qE[/tex]

where q is the charge and E the electric field. In this problem:

[tex]q = +e = +1.6\cdot 10^{-19} C[/tex] is the charge of the calcium ion

[tex]E=1.0 \cdot 10^7 N/C[/tex] is the magnitude of the electric field

Substituting,

[tex]F=(1.6\cdot 10^{-19}C)(1.0\cdot 10^7 N/C)=1.6\cdot 10^{-12} N[/tex]

2) Acceleration: [tex]2.5\cdot 10^{13} m/s^2[/tex]

The atomic mass of a calcium ion is approx. 40 a.m.u, this means that its mass is

[tex]m=40 \cdot (1.6\cdot 10^{-27}kg)=6.4\cdot 10^{-26} kg[/tex]

And so, the acceleration of the ion is given by Newton's second law:

[tex]a=\frac{F}{m}=\frac{1.6\cdot 10^{-12}N}{6.4\cdot 10^{-26} kg}=2.5\cdot 10^{13} m/s^2[/tex]

3) Yes

Explanation: a particle with same charge (+e) of the calcium ion could have the same acceleration of the calcium ion if it has exactly the same mass. In fact, the acceleration depends only on two factors: the mass and the force, so it both are the same, than the acceleration does not change.

4) The mass of the particle

In fact, the acceleration of the particle is given by:

[tex]a=\frac{F}{m}[/tex]

where F is the electric force and m the mass. Therefore, if the mass changes ,the acceleration changes as well.

A particle with the same mass and charge as calcium could have a different acceleration.

Let us recall that the electric field strength is the magnitude of the electric field at a point. Mathematically;

F = qE

F = electric force

q = charge on the +e ion

E electric field strength

F = 1.0 x 10^7 N/C x 1.6 x 10^-19 C

F = 1.6 x 10^-12 N

Since;

F =  ma

a = F/m = 1.6 x 10^-12 N/40(1.6 x 10^-27)

a = 2.5 x 10^13 ms-2

A particle with the same mass and charge as calcium could have a different acceleration. If the mass of the particle changes, the acceleration of the particle changes as also.

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What units are used to express pressure measurements

Answers

The three units used to express pressure are pascal (Pa), atmosphere (atm), and Hg (torr).

The three units are pascal(pa) atmosphere (atm) and hg (torr)

What quantities determine the resistance of a piece of material? Choose all that apply.The voltage across the materialThe type of materialThe current flowing through the piece of materialThe cross-sectional area of the piece of materialThe length of the piece of material

Answers

Answer;The type of materialThe cross-sectional area of the piece of materialThe length of the piece of materialExplanation;

The resistance is a measure of how the material impedes the flow of electrons through it. There are several factors that affect the resistance of a wire or a material.

The four main factors which affect the resistance of a material are;

The length of the wireThe thickness of the wireThe temperature of the wireThe type of material the wire is made of.
Final answer:

The resistance of a piece of material is determined by its type of material, cross-sectional area, and length. Voltage and current are related to resistance through Ohm's law but do not determine it. Temperature can also affect resistance.

Explanation:

The quantities that determine the resistance of a piece of material are:


The type of material: Different materials have different inherent resistivities, which affect the level of resistance offered by the material.
The cross-sectional area of the material: The resistance is inversely proportional to the area. A larger cross-sectional area allows for more current to flow, reducing resistance. The length of the piece of material: Resistance is directly proportional to the length. The longer the material, the higher the resistance, as there is more material for the electrical current to pass through, and more opportunity for collisions that impede flow.

It is to be noted that the voltage across the material and the current flowing through do not determine the resistance of a material but are related to it by Ohm’s law, which states that voltage (V) is the product of current (I) and resistance (R): V = IR.

Additionally, temperature can also influence resistance, generally increasing it in conductors as temperature rises.

What factors affect how strong the electric force is between two charged objects

Answers

The size of the electric force between two objects is affected by the strength of the charge and the distancebetween the objects. Objects with strong positive and negative charges will have a greater electric force. As the distance between the objects decreases, the electrical force increases.

The size of the electric force between two objects is affected by the strength of the charge and the distance between the objects. Objects with strong positive and negative charges will have a greater electric force. As the distance between the objects decreases, the electrical force increases.

If 1495 j of heat is needed to raise the temperature of a 339 g sample of a metal from 55.0°c to 66.0°c, what is the specific heat capacity of the metal

Answers

Specific heat of a substance can be calculated using the equation q=mst, where “q” is heat applied to the system, “m” is the mass of the substance, “s” is the specific heat, and “t” is the change in temperature. In this case,

q=mst

(1495 J)=(339 g)(s)(+11 degrees C)

s=0.401 J/g•degrees C.

The specific heat of this substance is 0.401 J/g•degrees C). However, the problem is asking for the heat capacity of the metal, which is defined as C=ms using the same definitions as above. In this case, the heat capacity of the metal works out to be 135.91 J/g.

Hope this helps!

Determine the pressure acting on a surface of area equal to 2 m2 if the force applied to the surface is 4 N

Answers

Answer:

2 N/m²

Explanation:

Pressure is defined as the force acting on a unit area .

Therefore;

Pressure = Force /Area

Force = 4 N

Area = 2 m²

Therefore;

Pressure = 4 N/ 2m²

               = 2 N/m²

Individual sports are different from team sports in that they require an internal focus and dialogue. Please select the best answer from the choices provided. T F

Answers

Answer:

true

Explanation:

It is true that individual sports is different from team sports.

Individual sports depend upon the individual's hard work, focus,determination only he is responsible for his fate.

when we talk about team sports it is about co-ordination , team brilliance individual cannot team sport alone every one have to contribute for the team to succeed.

Individual sports are different from team sports in that they require an internal focus and dialogue. The statement is true.

Individual sports and team sports do have distinct characteristics, and one of the notable differences is the emphasis on internal focus and dialogue in individual sports.

In individual sports, athletes compete on their own without relying on teammates. They have sole responsibility for their performance, decision-making, and strategy execution.

As a result, individual athletes often rely heavily on their internal focus to stay motivated, maintain concentration, and push themselves to perform at their best.

They engage in internal dialogues to manage their thoughts, emotions, and self-motivation throughout the competition. This internal focus and dialogue help them stay focused, make quick decisions, and adapt to changing circumstances.

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A gas heated to millions of degrees would emit

Answers

A gas heated to millions of degrees would emit mostly x-rays.

High-energy electromagnetic waves would be produced by a gas that has been heated to millions of degrees in terms of thermal radiation. The atoms and molecules included in a gas experience collisions, transitions, and ionisation processes as its temperature rises.

A wide range of electromagnetic radiation, including visible light, ultraviolet (UV) radiation, and X-rays, are produced as a result of these powerful interactions. The gas composition, temperature, and other parameters affect the precise wavelengths and intensities of the radiation that is emitted.

This effect has been seen in a variety of astrophysical settings, including high-temperature plasmas in laboratory studies, the highly hot and active areas of stars, supernovae, and accretion discs surrounding black holes.

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Which of the following is the best thermal insulator?

A.Air

B.Aluminum

C.Iron

D.Water

Answers

B. Aluminum is possibly correct

In a parallel circuit the current A stays in one path B splits and goes through two components C makes one circle

Answers

Answer:

B splits and goes through two components

Explanation:

- A series circuit is a circuit in which the components are all connected along the same branch: as a result, the current flowing through the components is the same, while the sum of the potential differences across each component is equal to the emf of the battery

- A parallel circuit is a circuit consisting of separate branches, so that each branch has a potential difference equal to the emf of the battery. As a result, in such a circuit the current in the circuit splits and goes through the different branches/components.

So, the correct answer is

B splits and goes through two components

In a parallel circuit, the current splits and travels through multiple components simultaneously. This results in a division of current among different pathways while maintaining consistent voltage across each component. Option B is correct.

In a parallel circuit, the current splits and goes through two components. This is because a parallel circuit provides multiple paths for electricity to flow. Each component in a parallel circuit is connected to the same two points, leading to a division of current among the different paths. However, the voltage across each component remains the same.

Resistors in parallel serve as current dividers, reducing the overall resistance compared to a single pathway. This characteristic allows parallel circuits to maintain the same potential difference across each branch, equal to the potential difference across the power source. Consequently, the sum of the currents across all branches equals the total current supplied to the circuit.

Parallel circuits find applications in everyday systems, such as building lighting, where several devices operate independently on the same voltage level. The setup of these circuits ensures a consistent voltage supply and allows individual components to function even if one branch fails.

Hence, B. is the correct option.

An object of mass m rests on a flat table. The earth pulls on this object with a force of magnitude mg. What is the reaction force to this pull?

Answers

The reaction force of the object on the flat table will be in upward direction with the same magnitude mg.

Explanation:

According to third law of motion, every action has equal and opposite reactions. So here, the action is the gravitational pull acting downward on the object kept on table with a magnitude of mg.

So as per third law, the reaction of the object will be in opposite direction to the action i.e., the pull will be in the upward direction as reaction to the gravitational pull toward downward direction and the magnitude should be same as mg.

Thus, the reaction exerted by the object on the table for the action of gravitational force of magnitude will be the upward pull of the object from the table with the magnitude mg and as both the action and reaction will be canceling each other, the object will remain at the same position on the table without any motion as there is no unbalanced force in the system.

Final answer:

The reaction force to Earth's gravitational pull on an object is the normal force, which has the same magnitude as the object's weight but in the opposite direction, thereby allowing the object to remain at rest on a table.

Explanation:

The reaction force to the pull of Earth on an object with mass m is known as the normal force. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. Therefore, if the Earth is pulling on the object with a force of mg, where g is the acceleration due to gravity (approximately 9.80 m/s² on Earth), then the table must be pushing up on the object with an equal force. This upward force is the normal force exerted by the table on the object, and it has the same magnitude as the weight of the object but in the opposite direction. Thus, the reaction force is mg directed upward. This concept is also evident when we consider the object's weight—the gravitational force on a mass m—which is calculated using the formula F = ma = mg. If there were no reaction force, the object would not remain at rest on the table.

A bowling ball of mass mb = 3.1 kg is rolled down the lane with a velocity of v1 = 2.5 m/s. It strikes a single remaining pin mp = 0.67 kg head on. After the collision the bowling ball has a velocity (in the same direction) of v2 = 1.95 m/s. How fast will the pin move immediately after it is hit?

Answers

Answer:

pin will move in the direction of motion of ball with speed

v = 2.54 m/s

Explanation:

As we know that there is no force on the pin + bowling ball system

So we will have net momentum before and after collision will remain conserved

so we will say that

[tex]m_b v_i = m_b v_{1f} + m_p v_{2f}[/tex]

now plug in all data into the above equation

[tex]3.1(2.5) = 3.1(1.95) + 0.67 v[/tex]

[tex]3.1(2.5 - 1.95) = 0.67 v[/tex]

[tex]v = \frac{3.1(2.5 - 1.95)}{0.67}[/tex]

[tex]v = 2.54 m/s[/tex]

Here, we are required to determine how fast the pin will move after it is hit.

The pin will move with a velocity of;.

v(p) = 2.54m/s

From the question, it is evident the pin is stationary prior to the collision.

During a collision, Momentum is conserved.

Therefore,

momentum before collision = momentum after collision.

{m(b)×v1} + {m(p)×0} = {m(b)×v2} + {m(p)×v(p)}

We then have;

(3.1 × 2.5) = (3.1 × 1.95) + (0.67 × v(p))

Therefore; 0.67v(p) = 1.705

v(p) = 1.705/0.67

Therefore, the pin will move with a velocity of;

v(p) = 2.54m/s

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