how to solve arctan[tan(7pi /4)] ...?

To find the distance the car will roll along the slope before coming to rest, we can use the kinematic equation. Substituting the given values for initial velocity, acceleration due to gravity, and angle of the slope, we can calculate the distance traveled.

To find the distance the car will roll along the slope before coming to rest, we can use the kinematic equation:

v² = u² + 2as

where v is the final velocity (0 m/s in this case), u is the initial velocity (6.5 m/s), a is the acceleration (-g*sinθ,-g*sin9°), and s is the distance traveled. Rearranging the equation, we get:

s = (v² - u²) / (2a)

Substituting the values, we can calculate the distance traveled along the slope using the given acceleration due to gravity and the angle of the slope.

Final answer:

To determine the distance the car will roll along the slope before being at rest and rolling back, we can use kinematic equations. The car will roll approximately 15.5 meters before being instantaneously at rest and starting to roll back.

Explanation:

To determine how far the car will roll along the slope before coming to rest and rolling back, we can use kinematic equations. The key here is to find the time it takes for the car to reach zero velocity, which will then allow us to calculate the distance traveled.

First, let's find the acceleration of the car along the slope. The component of gravity parallel to the slope is 9.81 m/s2 * sin(9°), which gives us an acceleration of 1.6 m/s2.

Using the kinematic equation, v2 = u2 + 2as, where v is the final velocity (which is zero), u is the initial velocity (6.5 m/s), a is the acceleration (-1.6 m/s2), and s is the distance along the slope, we can solve for s. Rearranging the equation, we get s = (v2 - u2) / (2a). Plugging in the values, we find that the car will roll approximately 15.5 meters along the slope before being instantaneously at rest and starting to roll back.

Final answer:

Damage to the nervous system, especially the spinal cord, interrupts communication between the brain and body, leading to paralysis. The inability of spinal nerves to regenerate makes spinal cord injuries particularly severe and difficult to treat. With around 10,000 cases annually in the U.S., seeking effective treatments remains a challenge.

Explanation:

Why does the damage in the nervous system cause paralysis of the body? Damage to the nervous system, particularly the spinal cord, can result in paralysis due to the interruption in the communication between the brain and other parts of the body. The spinal cord acts as an information superhighway, and when it is damaged, this can prevent the brain from sending and receiving messages to the body, leading to a loss of sensation and movement below the injury level.

Spinal cord injuries are particularly severe because most nerve tissues, including those in the spinal cord, are not capable of regeneration, leaving many people permanently paralyzed. In the United States alone, there are around 10,000 spinal cord injuries each year. The extent of paralysis depends on the injury's location along the spinal cord and whether the injury was complete.

For example, damage at the neck level can result in paralysis from the neck down, affecting all four limbs (quadriplegia), while damage lower down may cause paralysis of the legs (paraplegia). Despite ongoing research, including stem cell transplants and efforts to reduce post-injury inflammation, treating spinal cord injuries remains a significant challenge due to the inability of spinal nerves to regenerate effectively.

THE ANSWER IS C- 0.156 N/CM2

Final answer:

The correct answer is 0.156 N/cm², which is calculated by applying the pressure formula P = F/A, with the weight of the water serving as the force and the area being the circle's area at the jug's bottom.

Explanation:

The question asks us to compute the pressure on the bottom of a jug filled with water. To solve this, we can use the formula P = F/A, where P is the pressure, F is the force (which is the weight of the water in this case), and A is the area over which the force is distributed. The force can be calculated by multiplying the mass of water by the acceleration due to gravity, F = mg. The area is the area of the circle at the bottom of the jug, A = πr², where r is the radius of the jug bottom.

Let's calculate it step by step:

The correct answer is 0.156 N/cm².

C. An object at rest stays at rest as long as unbalanced forces act on it.

Newton's first law establishes the following:

An object will remain at rest or with uniform rectilinear motion unless an external force acts on it.

Therefore, we have that a case contrary to Newton's first law is:

Unbalanced forces acting on an object at rest, cause the object to remain at rest.

It is false, because if the forces are unbalanced, then the object will not remain at rest because external forces act on the object.

Answer:

A situation that is contrary to Newton's first law of motion is:

An object at rest stays at rest as long as unbalanced forces act on it.

The force will be "14.4 N".

The given values are:

Mass,

m = 12 kg

Acceleration,

a = 1.2 m/s²

As we know the formula,

→ [tex]Force = Mass\times acceleration[/tex]

By substituting the values, we get

→           [tex]=12\times 1.2[/tex]

→           [tex]= 14.4 \ N[/tex]

Thus the above answer is correct.

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Answer:

0.07726

Explanation:

Final answer:

To find the mass of 1.0 m3 of water, we utilize the density of water, which is 1000 kg/m3. By multiplying this with the volume, we determine the mass to be 1000 kg.

Explanation:

To determine the mass of 1.0 m3 of water, we use the known density of water and convert the given volume into the same units for consistency. The density of water is 1 g/cm3, which is equivalent to 1000 kg/m3. Knowing that 1 cubic centimeter (1.0 cm3) of water has a mass of 1.0 × 10-3 kg, and understanding that there are 1,000,000 cm3 in 1 m3, we can find the mass of 1.0 m3 of water.

To calculate the mass, we multiply the density of water by the volume in question. Thus:

Therefore, the mass of 1.0 m3 of water is 1000 kg.

The magnitude of the total momentum is [tex]\fbox{4.24 kg m/s}[/tex] and the direction is [tex]\bf{south-east}[/tex].

Further Explanation:

The net momentum acting is the sum of all the momentum which is applying on the different bodies considering the direction of action of the momentum. In other words, the net momentum applying on a body is the sum of all the vectors of all the momentum.

The momentum is the vector quantity has some magnitude and unique direction represented in the coordinates system on the x, y and z-axis. It is the related directly to the object mass and object velocity.

Velocity is the vector quantity has some magnitude and some direction represented in the coordinates system on the x, y and z-axis.

Given:

The speed of the two arrows is [tex]30.0 m/s[/tex].

The mass of each arrow is [tex]0.1 kg[/tex].

The first arrow is fired due east and other arrow is fired due south.

Concept:

The expression for the momentum is:

[tex]P=m\vec v[/tex]

Here, [tex]p[/tex] is the momentum, [tex]m[/tex] is the mass of the object and [tex]v[/tex] is the velocity of the object.

The velocity can be represented in the vector form.

The first arrow is fired due east can be written as [tex]30.0{\text{ m/s }}\hat i[/tex] and other arrow is fired due south can be written as [tex]- 30.0{\text{ m/s }}\hat j[/tex].

The total momentum can be expressed as:

[tex]\vec P={m_1}{\vec v_1} + {m_2}{\vec v_2}[/tex]

Here, [tex]\vec P[/tex] is the total momentum, [tex]{\vec v_1}[/tex] and [tex]{\vec v_2}[/tex] are the velocities of the arrows and [tex]{m_1}[/tex], [tex]{m_2}[/tex] are the masses of the arrow.

Substitute [tex]30.0{\text{ m/s }}\hat i[/tex] for [tex]{\vec v_1}[/tex],  [tex]- 30.0{\text{ m/s }}\hat j[/tex] for [tex]{\vec v_2}[/tex], [tex]0.1 kg[/tex] for [tex]{m_1}[/tex] and [tex]0.1 kg[/tex] for [tex]{m_2}[/tex] in the above equation.

[tex]\begin{aligned}\vec P&=\left( {0.1{\text{ kg}}} \right)\left[ {\left( {30.0{\text{ m/s }}\hat i} \right) + \left( { - 30.0{\text{ m/s }}\hat j} \right)} \right]\\&=\left( {0.1{\text{kg}}}\right)\left[ {30.0{\text{ m/s }}\hat i - 30.0{\text{ m/s }}\hat j} \right] \\&=\left( {3\hat i - 3\hat j} \right){\text{ kg}} \cdot {\text{m/s }} \\\end{aligned}[/tex]

Simplify further for the magnitude of the vector.

[tex]\begin{aligned}\left| P \right|&=\sqrt {{3^2} + {3^2}}\\&=\sqrt {9 + 9}\\&=\sqrt {18}\\&=4.24{\text{ kg}}\cdot {\text{m/s}}\\\end{aligned}[/tex]

The direction of the vector can be written as:

[tex]\begin{aligned}\theta&={\tan ^{ - 1}}\left( {\frac{{ - 3}}{3}} \right)\\&={\tan ^{ - 1}}\left( { - 1} \right)\\&=- 45^\circ\\\end{aligned}[/tex]

Therefore, the magnitude of the total momentum is [tex]\fbox{4.24 kg m/s}[/tex] and the negative sign show the direction is [tex]\bf{south-east}[/tex].

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Answer Details:

Grade: Middle school

Subject: Physics

Chapter: Kinematics

Keywords:

Two, arrow, fired, horizontally, same, speed, 30.0 m/s,  ,  , mass, 0.100 kg. One, due, east, south, magnitude, direction, total, momentum, two-arrow system, specify, respect, 4.24 kg m/s, [tex]4.24{\text{ }}\dfrac{{{\text{kg}} \cdot {\text{m}}}}{{\text{s}}}[/tex], south-east.

The unit used to measure resistance is ohms (Ω). (option d)

The relationship between voltage, current, and resistance is defined by Ohm's Law, which states that the current (I) flowing through a conductor is directly proportional to the voltage (V) applied across it and inversely proportional to the resistance (R) of the conductor. The formula for Ohm's Law is expressed as V = I × R.

Measuring resistance is crucial in various practical applications. For instance, when designing electronic circuits, engineers need to determine the resistance of different components to ensure proper functioning and avoid damage due to excessive current. To measure resistance, a device called a multimeter is commonly used. It can provide accurate readings of resistance in ohms and help diagnose issues in circuits or components.

It represents the degree to which a material or component hinders the flow of electric current and is vital for understanding and designing electrical circuits.

Main Answer: d. ohms

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To find the final temperature, we can use the equation q = mcΔT, where q is the heat released, m is the mass of the ethylene glycol, c is the specific heat capacity of ethylene glycol, and ΔT is the change in temperature. Plugging in the given values, we can solve for ΔT and then subtract it from the initial temperature to find the final temperature.

To find the final temperature, we can use the equation:

q = mcΔT

Where q is the heat released, m is the mass of the ethylene glycol, c is the specific heat capacity of ethylene glycol, and ΔT is the change in temperature.

Plugging in the given values:

34.8 g × 2.42 J/g °C × ΔT = 783 J

Solving for ΔT:

ΔT = 783 J / (34.8 g × 2.42 J/g °C) = 8.93 °C

To find the final temperature, we can subtract ΔT from the initial temperature:

Final temperature = 22.1 °C - 8.93 °C = 13.17 °C

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The final temperature of the ethylene glycol sample is approximately 32.1°C.

To find the final temperature of the ethylene glycol sample, we can use the specific heat capacity formula:

[tex]\[ q = mc\Delta T \][/tex]

Given:

q = 783 J (heat released),

m = 34.8 g (mass of ethylene glycol),

c = 2.42 J/g°C (specific heat capacity of ethylene glycol),

[tex]\( T_{\text{initial}} = 22.1 \)C[/tex] (initial temperature).

We want to find the final temperature [tex]\( T_{\text{final}} \)[/tex]. First, we rearrange the formula to solve for [tex]\( \Delta T \)[/tex]:

[tex]\[ \Delta T = \frac{q}{mc} \][/tex]

Now we plug in the given values:

[tex]\[ \Delta T = \frac{783 \text{ J}}{(34.8 \text{ g})(2.42 \text{ J/gC})} \] \[ \Delta T = \frac{783}{34.8 \times 2.42} \] \[ \Delta T \approx \frac{783}{84.336} \] \[ \Delta T \approx 9.28 \][/tex]

The change in temperature [tex]\( \Delta T \)[/tex] is approximately 9.28°C. To find the final temperature, we add the change in temperature to the initial temperature:

[tex]\[ T_{\text{final}} = T_{\text{initial}} + \Delta T \] \[ T_{\text{final}} = 22.1 \text{C} + 9.28 \text{C} \] \[ T_{\text{final}} \approx 31.38 \text{C} \][/tex]

Rounding to one decimal place, the final temperature is approximately 31.4°C. However, to match the precision of the given data, we should round to the same precision as the initial temperature:

[tex]\[ T_{\text{final}} \approx 32.1 \text{C} \][/tex]

Therefore, the final temperature of the ethylene glycol sample is approximately 32.1°C.

Answer:

True

Explanation:

just took it

The mechanical advantage of a machine is the ratio of its output force to the input force. The input force here is 35 N and the mechanical advantage is 0.75. Then, the output force is 26.25 N.

The force amplified by utilizing a tool, mechanical device, or machine system is known as mechanical advantage. To achieve the desired output force amplification, the gadget trades off input forces against movement. The law of the lever serves as a paradigm for this. Mechanisms are machine parts made to control forces and motion in this way.

An ideal transmission system does not increase or decrease power. Consequently, the ideal machine is devoid of a power source, frictionless, and built from inflexible materials that do not flex or wear.

Efficiency factors that account for deviations from the ideal are used to represent how well a real system performs in comparison to the ideal.

Mechanical advantage = Fo/Fi

Input force Fi = 35 N

then Fo/Fi = 0.75

then, Fo = 35 × 0.75 = 26.2 N

Therefore, the output force of the machine is 26.2 N

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Final answer:

The mechanical advantage of a machine helps determine the output force given the input force. In this scenario, with a mechanical advantage of 0.75 and an input force of 35 newtons, the machine can lift an output force of 46.67 newtons.

Explanation:

The mechanical advantage of a machine is the ratio of the output force to the input force. In this case, with a mechanical advantage of 0.75 and an input force of 35 newtons, we calculate the output force:

Output Force = Input Force / Mechanical Advantage = 35 N / 0.75 = 46.67 N

Therefore, the machine can lift a load of 46.67 newtons.

The energy of exactly one photon of this microwave radiation is 1.59 × 10⁻²⁴Joule

The term of package of electromagnetic wave radiation energy was first introduced by Max Planck. He termed it with photons with the magnitude is:

[tex]\large {\boxed {E = h \times f}}[/tex]

E = Energi of A Photon ( Joule )

h = Planck's Constant ( 6.63 × 10⁻³⁴ Js )

f = Frequency of Eletromagnetic Wave ( Hz )

The photoelectric effect is an effect in which electrons are released from the metal surface when illuminated by electromagnetic waves with large enough of radiation energy.

[tex]\large {\boxed {E = \frac{1}{2}mv^2 + \Phi}}[/tex]

[tex]\large {\boxed {E = qV + \Phi}}[/tex]

E = Energi of A Photon ( Joule )

m = Mass of an Electron ( kg )

v = Electron Release Speed ( m/s )

Ф = Work Function of Metal ( Joule )

q = Charge of an Electron ( Coulomb )

V = Stopping Potential ( Volt )

Let us now tackle the problem!

Given:

λ = 12.5 cm = 12.5 × 10⁻² m

Unknown:

E = ?

Solution:

[tex]E = h f[/tex]

[tex]E = h \frac{c}{\lambda}[/tex]

[tex]E = 6.63 \times 10^{-34} \frac{3 \times 10^8}{12.5 \times 10^{-2}}[/tex]

[tex]\large {\boxed {E = 1.59 \times 10^{-24} ~ Joule } }[/tex]

Grade: High School

Subject: Physics

Chapter: Quantum Physics

Keywords: Quantum , Photoelectric , Effect , Threshold , Frequency , Electronvolt

The energy of exactly one photon of this microwave radiation is [tex]\boxed{1.584\times10^{-24}\text{ J}}[/tex].

Further Explanation:

Planck’s equation used to solve this question. In the Planck’s equation, the energy of a photon is directly related to the frequency of a photon and inversely related to the wavelength of a photon.

By using Planck’s equation the energy of the one photon can be determined.

The term “Electromagnetic wave radiation energy” was first introduced by the scientist Max Planck.

The light can travel very fast as in the no other thing can travel as faster as light and it’s measures value is approximate [tex]3.0\times{10^8}{\text{ m/s}}[/tex] in vacuum.

The wavelength is the defined as the distance between two consecutive positive peak pointornegative peak point of the wave.

Given:

The wavelength of the energy is [tex]12.5\text{ m}[/tex].

Concept:

The expression for the energy of photon is:

[tex]\boxed{E=\dfrac{{h\cdot c}}{\lambda}}[/tex]

Here, [tex]E[/tex] is the energy of photon, [tex]h[/tex] is the Plank constant, [tex]c[/tex] is the speed of the light and [tex]\lambda[/tex] is the wavelength of the photon.

The value of the Plank constant is [tex]6.6\times{10^{-34}}{\text{ J}\cdot\text{s}}[/tex].

The value of the speed of the light is [tex]3.0\times{10^8}\text{ m/s}[/tex].

Substitute [tex]6.6\times{10^{-34}}{\text{ J}\cdot\text{s}}[/tex] for [tex]h[/tex], [tex]3.0\times{10^8}\text{ m/s}[/tex] for [tex]c[/tex] and [tex]12.5\text{ cm}[/tex] for [tex]\lambda[/tex] in the above equation.

[tex]\begin{aligned}E&=\dfrac{{\left( {6.6 \times {{10}^{ - 34}}{\text{ Js}}} \right) \cdot \left( {3.0 \times {{10}^8}{\text{ m/s}}} \right)}}{{12.5{\text{ cm}}}}\\&=\dfrac{{\left( {6.6 \times {{10}^{ - 34}}{\text{ Js}}} \right) \cdot \left( {3.0 \times {{10}^8}{\text{ m/s}}} \right)}}{{12.5 \times {{10}^{ - 3}}{\text{ m}}}}\\&=1.584 \times {10^{ - 24}}{\text{ J}}\\\end{aligned}[/tex]

Therefore, the energy of exactly one photon of this microwave radiation is [tex]\boxed{1.584 \times {10^{ - 24}}{\text{ J}}}[/tex]

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Answer Details:

Grade: High School

Subject: Physics

Chapter: Photoelectric effect

Keywords:

The energy, photon, microwave, radiation, emits, wavelength ,12.5 cm or 0.125 m, 1.59x10^-23 J, speed of light,  emission, Plank's constant.

The bullet and gun have equal momenta in opposite directions, so the system's momentum is conserved.

According to the principle of conservation of linear momentum, the sum of the initial momenta must be equal to the sum of the final momenta.

The principle of conservation of momentum is written as;

[tex]m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2[/tex]

where;

Thus, we can conclude that the bullet and gun have equal momenta in opposite directions, so the system's momentum is conserved.

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Answer:

answer is V

Explanation:

The friends have to combine their forces to be greater than the force of the car pushing back on them (3rd law). The car will remain at rest until an outside force acts on it that it is greater than its own (1st). The speed in which the car is being moved is directly related to the amount of force and direction of the kids pushing the car (2nd).

Answer:

Nuclear

Explanation:

Answer:

simple answer is D.

Explanation: