Baseball scouts often use a radar gun to measure the speed of a pitch. One particular model of radar gun emits a microwave signal at a frequency of 10.525 GHz. What will be the increase in frequency if these waves are reflected from a 95.0mi/h fastball headed straight toward the gun?

Q: a silver ingot has a volume of 53.6 cm³ and weighs 500g. what is the desity in grams per cubic centimeter.

Answer:

9.33 kg/m³

Explanation:

Density: This can be defined as the ratio of the mass of a substance and it's volume.

The Formula for Density is given as,

D = m/v ..................... Equation 1

Where D = Density of the silver ingot, m = mass of the silver ingot, v = volume of the silver ingot.

Given: m = 500 g, v = 53.6 cm³

Substitute into equation  1

D = 500/53.6

D = 9.33 kg/m³.

Hence the density of the ingot = 9.33 kg/m³.

Final answer:

The density of the silver ingot, which has a mass of 500 g and a volume of 53.6 cm³, is found by dividing the mass by the volume. The calculation yields a density of approximately 9.33 g/cm³ for the silver ingot.

Explanation:

The student is asking for the density of a silver ingot, which is a measurement of mass per unit volume of a substance. The formula for calculating density is mass divided by volume. Given that the silver ingot has a mass of 500 g and a volume of 53.6 cm³, we can determine its density using this formula.

To find the density of the silver ingot, you would:

Answer:

Explanation:

Height covered = 12m

time to fall by 12 m

s = 1/2 gt²

12 = 1/2 g t²

t = 1.565 s

Horizontal distance of throw

= 8.5 x 1.565

= 13.3 m

This distance is to be covered by dog during the time ball falls ie 1.565 s

Speed of dog required = 13.3 / 1.565

= 8.5 m /s

b ) dog will catch the ball at a distance of 13.3 m .

Answer:

[tex]P=1139.16384mmHg[/tex]

Explanation:

Given data

[tex]R=0.08206(\frac{L.Atm}{mol.K} )\\Density=2.697g/L\\Temperature=298K\\f.wt=44(g/mol)\\[/tex]

To find

Pressure

Solution

From Ideal gas law we know that

[tex]PV=nRT\\P=(nR\frac{T}{V} )=(R(\frac{mass}{f.wt} )(\frac{T}{V} ))\\P=R(\frac{mass}{volume}) (\frac{T}{f.wt} )=R(Density)(\frac{T}{f.wt} )[/tex]

Substitute the given values to find pressure

So

[tex]P=(0.08206\frac{L.Atm}{mol.K} )(2.697g/L)(298K)(44g/mol)^{-1}\\ P=1.4989Atm\\[/tex]

Convert Atm to mmHg

Multiply the pressure values by 760

So

[tex]P=1139.16384mmHg[/tex]

Answer:

In the last second, the object traveled 45.6 m.

Explanation:

Hi there!

The equation of the height of the object at a time t is the following:

h = h0 + v0 · t + 1/2 · g · t²

Where:

h =height of the object at time t.

h0 = initial height.

v0 = initial velocity.

t = time.

g = acceleration due to gravity (-9.8 m/s²).

First, let's find how much time it takes the object to reach the ground. For that, we have to find the value of "t" for which h = 0.

h = h0 + v0 · t + 1/2 · g · t²

Since the object is dropped and not thrown (v0 = 0).

h = h0 + 1/2 · g · t²

0 m  = 128 m - 1/2 · 9.8 m/s² · t²

-128 m / -4.9 m/s² = t²

t = 5.1 s

Now, let's find the height of the object 1 s before reaching the ground (at t = 4.1 s):

h = h0 + v0 · t + 1/2 · g · t²

h = 128 m - 1/2 · 9.8 m/s² · (4.1 s)²

h = 45.6 m

Then, in the last second (from 4.1 s to 5.1 s) the object traveled 45.6 m

When measuring weight on a scale that is accurate to the nearest 0.1

pound, the real limits for the weight of 145 pounds is 144.9- 145.1

This is an instrument which is used to measure the weight of objects. There

may be differences in the measurement as a result of air interference and

other factors.

We were told that the accuracy is to the nearest 0.1 pound which means

= 145± 0.1

= (145-0.1) - (145+0.1)

= 144.9 - 145.1

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The real limits for the weight of 145 pounds on a scale accurate to the nearest 0.1 pound are 144.95 to 145.05 pounds.

When measuring weight on a scale that is accurate to the nearest 0.1 pound, the real limits for the weight of 145 pounds would be 144.95 to 145.05 pounds. This is because the scale is accurate to the tenths place, meaning it can measure weights up to one decimal place. In this case, the weight of 145 pounds would be rounded to 145.0 pounds. Therefore, the real limits would be 144.95 pounds (145.0 - 0.05) to 145.05 pounds (145.0 + 0.05).

Answer:

R =  16.67 m

Explanation:

Given:

- Initial Temperature T_i = 20 C

- Thickness of both strips t = 0.001 m

- Final Temperature T_f = 30 C

- Length of the strip L = 0.1 m

- coefficient of linear expansion for brass a_b = 19*10^-6

- coefficient of linear expansion for steel a_s = 13*10^-6

Find:

What is the radius of curvature of this arc R?

Solution:

- The radius of curvature R in relation to dT and a_b, a_s:

                               R = t / dT*(a_b - a_s)

                               R = 0.001 / (30-20)*(19-13)*10^-6

                               R =  16.67 m

Answer:

The average acceleration during the 6.0 s interval was -27 m/s².

Explanation:

Hi there!

The average acceleration is defined as the change in velocity over time:

a = Δv/t

Where:

a = acceleration.

Δv = change in velocity = final velocity - initial velocity

t = elapsed time

The change in velocity will be:

Δv = final velocity - initial velocity

Δv = -74 m/s - 87 m/s = -161 m/s

(notice the negative sign of the velocity that is in opposite direction to the direction considered positive)

Then the average acceleration will be:

a = Δv/t

a = -161 m/s / 6.0 s

a = -27 m/s²

The average acceleration during the 6.0 s interval was -27 m/s².

Answer:

Part A : 5.) = 564.704 N*m²/C

Part B:  10.) = 179751.0 V/m

Explanation:

A) Applying Gauss'Law to the straight filament, using a cylindrical gaussian surface with the filament as the central axis of the surface, assuming that the electric field is normal to the surface (which means that no flux exist through the lids of the cylinder) and is constant at any point of the surface (except the lids where is 0), we can find the electric flux, as follows:

[tex]E*2*\pi *r*l = \frac{Qenc}{\epsilon 0} (1)[/tex]

where:

r is the radius of the cylinder = 0.05 m

l is the length of the cylinder = 0.01 m

Qenc, is the net charge on the filament enclosed by the gaussian surface

ε₀ = 8.8542*10⁻¹² C²/N*m²

In order to find the value of Qenc, we need to find first the linear charge density, as follows:

[tex]\lambda = \frac{Q}{L} =\frac{+3e-6C}{6m} = 5e-7 C/m[/tex]

The net charge enclosed by the gaussian surface will be just the product of the linear change density λ times the length of the gaussian surface:

[tex]Qenc = \lambda * l = 5e-7C/m * 0.01 m = 5e-9 C[/tex]

According Gauss ' Law, the net flux through the gaussian surface must be equal to the charge enclosed by the surface, divided by the permittivity of free space (in vacuum or air), as follows:

[tex]Flux = \frac{Qenc}{\epsilon 0} = \frac{5e-9C}{8.8542e-12 C2/N*m2} = 564.704 (N*m2)/C[/tex]

which is the same as the option 5.

B)  Repeating the equation (1) from above:

[tex]E*2*\pi *r*l = \frac{Qenc}{\epsilon 0} (1)[/tex]

we can solve for E, as follows:

[tex]E = \frac{Qenc}{2*\pi*r*l* \epsilon 0} = \frac{5e-9C}{2*\pi*(0.05m)*(0.01m)*8.8542e-12 C2/N*m2} = 179751.0 V/m[/tex]

which is the same as the option 10 of part B.

Answer:

Explanation:

Given

velocity of diver [tex]u=-10\ m/s[/tex] i.e. downward motion

acceleration due to gravity [tex]a=g=-9.8\ m/s^2[/tex]

time [tex]t=1.16\ s[/tex]

using equation of motion

[tex]y=ut+\frac{1}{2}at^2[/tex]

[tex]y=(-10)\cdot 1.16-\frac{1}{2}(-9.8)(1.16)^2[/tex]

[tex]y=-11.6-6.593[/tex]

[tex]y=-18.19\ m[/tex]

I.e. in downward direction                    

The displacement of the diver during the last 1.16 seconds of her dive is -11.6 meters. The negative sign indicates a downward movement.

In physics, displacement is the overall change in position of an object. It is calculated by multiplying velocity and time. In this case, the velocity of the diver is -10.0 m/s (a negative sign indicating downward motion) and the time is 1.16 s. To find the displacement, multiply the velocity and the time: (-10.0 m/s) × (1.16 s) = -11.6 m. The minus sign still indicates downward direction, and it means that the diver moved 11.6 meters downward in the last 1.16 seconds of her dive.

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Answer:

There is no force acting on the body.

Explanation:

Answer:

Explanation:

Given

Voltage of battery [tex]V=45\ V[/tex]

electric field(E) is given by  

[tex]E=|-\frac{dV}{dx}|[/tex]

i.e. Change in Potential over a distance x

(a)When Plate are separated by 3 cm apart

[tex]E=|\frac{45}{3\times 10^{-2}}|[/tex]

[tex]E=1500\ V/m[/tex]

(b)When Plates are 5 cm apart

[tex]E=|-\frac{45}{5\times 10^{-2}}|[/tex]

[tex]E=900\ V/m[/tex]

Force on electron is given by

[tex]F=charge\times Electric\ Field[/tex]

[tex]F=q\times E[/tex]

For case a

[tex]F=1.6\times 10^{-19}\times 1500[/tex]

[tex]F=24\times 10^{-17}\ N[/tex]

(b)[tex]F=1.6\times 10^{-19}\times 900=14.4\times 10^{-17}\ N[/tex]

Answer:

C)T

Explanation:

The period of a mass-spring system is:

[tex]T=2\pi\sqrt\frac{m}{k}[/tex]

As can be seen, the period of this simple harmonic motion, does not depend at all on the gravitational acceleration (g), neither the mass nor the spring constant depends on this value.

Answer

Given,

Periscope uses 45-45-90 prisms with total internal reflection adjacent to 45°.

refractive index of water, n_a = 1.33

refractive index of glass, n_g = 1.52

When the light enters the water, water will act as a lens and when we see the object from the periscope the object shown is farther than the usual distance.

Answer:

[tex]a=-3\ m/s^2[/tex]

Explanation:

Second Newton's Law

It allows to compute the acceleration of an object of mass m subject to a net force Fn. The relation is given by

[tex]F_n=m.a[/tex]

The net force is the sum of all vector forces applied to the object. The block has two horizontal forces applied (in absence of friction): The 30 N force acting to the right and the 60 N force to the left. The positive horizontal direction is assumed to the right, so the net force is

[tex]F_n=30\ N-60\ N=-30\ N[/tex]

Thus, the acceleration can be computed by

[tex]\displaystyle a=\frac{F_n}{m}=\frac{-30}{10}=-3\ m/s^2[/tex]

[tex]\boxed{\displaystyle a=-3\ m/s^2}[/tex]

The negative sign indicates the block is accelerated to the left

The block will experience an acceleration of 3.0 m/s² to the left, as calculated by using the net force (30 N leftward) divided by the mass of the block (10.0 kg).

To determine the acceleration of a 10.0 kg block on a smooth horizontal surface that is being acted upon by two forces, one must first find the net force acting on the block. In this scenario, there is a 30 N force acting to the right and a 60 N force acting to the left. The net force can be found by subtracting the smaller force from the larger one, which gives us a result of 60 N - 30 N = 30 N acting to the left.

Now, using Newton's second law of motion which states that F = ma (where F is the net force, m is the mass of the object, and a is the acceleration), we can solve for acceleration by rearranging the equation to a = F/m. Plugging the net force (F = 30 N) and the mass of the block (m = 10.0 kg) into the equation yields:

a = 30 N / 10.0 kg = 3.0 m/s²

The acceleration of the block will be 3.0 m/s², and since the net force is to the left, the acceleration will also be directed to the left.

Answer:

trajectory

Explanation:

according to issac newton plants are important

Final answer:

Using Bernoulli's equation and the continuity equation, we find that as the diameter of a pipe decreases, the velocity of the water increases, and to conserve the total mechanical energy, gauge pressure in the constricted segment decreases.

Explanation:

The situation described in the question can be analyzed using the principle of conservation of energy, specifically Bernoulli's equation for incompressible fluid flow. We are given that water flows at a speed of 5.9 m/s through a horizontal pipe of diameter 3.1 cm, and the gauge pressure is 1.5 atm. With the constriction of the pipe's diameter to 2.1 cm, we want to find the new gauge pressure of the water.

According to Bernoulli's equation, the total mechanical energy per unit volume is the same at all points along the streamline, i.e.,

[tex]P + \(\frac{1}{2}\)\(\rho\)v^2 + \(\rho\)gh = constant[/tex]

where P is the pressure, \(\rho\) is the density of the fluid, v is the flow velocity, g is acceleration due to gravity, and h is the elevation. For the situation described, h remains constant (horizontal pipe), and there is no change in the gravitational potential energy. Therefore, we can simplify the equation to:

[tex]P1 + \(\frac{1}{2}\)\(\rho\)v1^2 = P2 + \(\frac{1}{2}\)\(\rho\)v2^2[/tex]

Since the fluid is incompressible and the flow rate must be conserved, the velocity v2 in the constricted segment is determined by the continuity equation:

[tex]A_1v_1 = A_2v_2[/tex]

To solve this problem, we'll use the principle of continuity, which states that the product of cross-sectional area and velocity is constant for an incompressible fluid flowing through a tube. Mathematically, it can be expressed as:

Step 1: Find  [tex]\( v_2 \)[/tex]

Using the continuity equation:

[tex]\[ A_1 V_1 = A_2 V_2 \][/tex]

We can find [tex]\( v_2 \)[/tex] as:

[tex]\[ V_2 = \frac{\frac{\pi D_1^2}{4}}{\frac{\pi D_2^2}{4}} \times V_1 \]\[ V_2 = \frac{D_1^2}{D_2^2} \times V_1 \][/tex]

Since [tex]\( A = \frac{\pi D^2}{4} \)[/tex], we can rewrite the equation as:

[tex]\[ V_2 = \frac{\frac{\pi D_1^2}{4}}{\frac{\pi D_2^2}{4}} \times V_1 \]\[ V_2 = \frac{D_1^2}{D_2^2} \times V_1 \][/tex]

Now, let's plug in the values:

[tex]\[ V_2 = \frac{(0.031 \, \text{m})^2}{(0.021 \, \text{m})^2} \times 5.9 \, \text{m/s} \]\[ V_2 = \frac{0.000961 \, \text{m}^2}{0.000441 \, \text{m}^2} \times 5.9 \, \text{m/s} \]\[ V_2 = \frac{0.000961}{0.000441} \times 5.9 \, \text{m/s} \]\[ V_2 \approx 12.84 \, \text{m/s} \][/tex]

Step 2: Calculate   [tex]\( P_2 \)[/tex]

We'll use Bernoulli's equation, which states that the sum of pressure energy, kinetic energy, and potential energy per unit volume is constant along any streamline of flow. In this case, we'll ignore changes in height (assuming horizontal flow), and the equation simplifies to:

[tex]\[ P_1 + \frac{1}{2} \rho v_1^2 = P_2 + \frac{1}{2} \rho v_2^2 \][/tex]

Where:

- [tex]\( P_1 \)[/tex] is the initial pressure

-  [tex]\( P_2 \)[/tex] is the pressure in the constricted segment

- [tex]\( \rho \)[/tex]is the density of the fluid (we'll assume water,[tex]\( \rho = 1000 \, \text{kg/m}^3 \))[/tex]

-[tex]\( v_1 \) and \( v_2 \)[/tex] are initial and final velocities, respectively.

We rearrange this equation to solve for  [tex]\( P_2 \)[/tex]:

[tex]\[ P_2 = P_1 + \frac{1}{2} \rho v_1^2 - \frac{1}{2} \rho v_2^2 \][/tex]

Now, let's plug in the values:

[tex]\[ P_2 = P_1 + \frac{1}{2} \times 1000 \times (5.9)^2 - \frac{1}{2} \times 1000 \times (12.84)^2 \]\[ P_2 = P_1 + 17421.5 - 82626.24 \]\[ P_2 = P_1 - 65204.74 \][/tex]

Step 3: Convert  [tex]\( P_2 \)[/tex] to atmospheres (gauge pressure)

To express the pressure in atmospheres and considering atmospheric pressure as the baseline, we need to subtract the atmospheric pressure from [tex]\( P_2 \)[/tex]. Assuming atmospheric pressure is [tex]\( 101.3 \, \text{kPa} \) (or \( 101300 \, \text{Pa} \))[/tex]:

[tex]\[ P_{\text{gauge}} = \frac{P_2 - \text{atmospheric pressure}}{\text{atmospheric pressure}} \]\[ P_{\text{gauge}} = \frac{-65204.74 - 101300}{101300} \]\[ P_{\text{gauge}} \approx -1.64 \][/tex]

So, the gauge pressure in the constricted segment is approximately [tex]\( -1.64 \)[/tex] atmospheres.

Answer:

1.15 rad/s²

Explanation:

given,

angular speed of turntable = 45 rpm

                       =[tex]45\times \dfrac{2\pi}{60}[/tex]

                       =[tex]4.71\ rad/s[/tex]

time, t = 4.10 s

initial angular speed = 0 rad/s

angular acceleration.

[tex]\alpha = \dfrac{\omega_f-\omega_0}{t}[/tex]

[tex]\alpha = \dfrac{4.71-0}{4.10}[/tex]

[tex]\alpha = 1.15\ rad/s^2[/tex]

Hence, the angular acceleration of the turntable is 1.15 rad/s²

Answer:

[tex]v_0 = 3.53~{\rm m/s}[/tex]

Explanation:

This is a projectile motion problem. We will first separate the motion into x- and y-components, apply the equations of kinematics separately, then we will combine them to find the initial velocity.

The initial velocity is in the x-direction, and there is no acceleration in the x-direction.

On the other hand, there no initial velocity in the y-component, so the arrow is basically in free-fall.

Applying the equations of kinematics in the x-direction gives

[tex]x - x_0 = v_{x_0} t + \frac{1}{2}a_x t^2\\63 \times 10^{-3} = v_0t + 0\\t = \frac{63\times 10^{-3}}{v_0}[/tex]

For the y-direction gives

[tex]v_y = v_{y_0} + a_y t\\v_y = 0 -9.8t\\v_y = -9.8t[/tex]

Combining both equation yields the y_component of the final velocity

[tex]v_y = -9.8(\frac{63\times 10^{-3}}{v_0}) = -\frac{0.61}{v_0}[/tex]

Since we know the angle between the x- and y-components of the final velocity, which is 180° - 2.8° = 177.2°, we can calculate the initial velocity.

[tex]\tan(\theta) = \frac{v_y}{v_x}\\\tan(177.2^\circ) = -0.0489 = \frac{v_y}{v_0} = \frac{-0.61/v_0}{v_0} = -\frac{0.61}{v_0^2}\\v_0 = 3.53~{\rm m/s}[/tex]

Final answer:

The question is about projectile motion in Physics, requiring knowledge of equations of motion, range calculation, and trigonometry to find the release angle for an arrow to hit a target and resolve if it will clear an obstacle.

Explanation:

The subject of this question is Physics, specifically dealing with concepts related to projectile motion and the laws of motion. The grade level would likely be High School where students are typically introduced to these topics in a physics curriculum.

As an example, for the question where an archer shoots an arrow at a 75.0 m distant target with an initial speed of 35.0 m/s, one would need to use the equations of projectile motion to solve for the correct release angle. This involves breaking down the initial velocity into its horizontal and vertical components, using the range equation for projectile motion, and applying trigonometry. To determine whether the arrow will go over or under a branch 3.50 m above the release point, one would need to calculate the maximum height of the arrow's trajectory.

In scenarios such as these, understanding the principles of inertia, conservation of momentum, and the conversion of potential energy into kinetic energy are essential.

Answer:The temperature of the entire water sample after all of the ice has melted is  [tex]30.3^0C[/tex]

Explanation:

As we know that,  

[tex]Q=m\times c\times \Delta T=m\times c\times (T_{final}-T_{initial})[/tex].......(1)

where,

q = heat absorbed or released

[tex]m_1[/tex] = mass of ice = 21.5 g

[tex]m_2[/tex] = mass of water = 500.0 g

[tex]T_{final}[/tex] = final temperature = ?

[tex]T1 =\text {temperature of ice}= 0^oC[/tex]

[tex]T_2[/tex] = temperature of water =[tex]31.0^oC[/tex]

[tex]c_1[/tex] = specific heat of ice= [tex]2.1J/g^0C[/tex]

[tex]c_2[/tex] = specific heat of water = [tex]4.184J/g^0C[/tex]

Now put all the given values in equation (1), we get

[tex]21.5\times 2.1\times (T_{final}-0)=-[500.0\times 4.184\times (T_{final}-31.0)][/tex]

[tex]T_{final}=30.3^0C[/tex]

Thus the temperature of the entire water sample after all of the ice has melted is  [tex]30.3^0C[/tex]

Final answer:

The speed of the rocket 10 seconds after liftoff is 60 ft/s.

Explanation:

To find the speed of the rocket 10 seconds after liftoff, we can differentiate the equation for the height of the rocket with respect to time. In this case, the equation for the height of the rocket is given as h = 3t^2. Taking the derivative of this equation with respect to time will give us the rate of change of height with respect to time, which is the speed of the rocket. The derivative of 3t^2 with respect to t is 6t. Plugging in t = 10 into the derivative, we get 6(10) = 60.

Answer:

1) Temperature of the water bath rises

2) the piston moves out

3) 133 kJ of heat flows

Explanation:

Given:(Isobaric process)

1)

Since the whole setup is isolated and the heat is absorbed by the system therefore the the temperature of the water will go down.

2)

When the system absorbs heat its pressure has to be constant so the piston needs to move up outwards giving the inside gases more volume.

As ideal gas law equation:

[tex]P.V=m.R.T[/tex]

[tex]P=[/tex]absolute pressure of the gas

[tex]V=[/tex] volume of the gas

[tex]m=[/tex] mass of the gas

[tex]R=[/tex] universal gas constant

[tex]T=[/tex] absolute temperature of the gas

Since pressure, mass and gas constants are the constant value we observe that: [tex]T\propto V[/tex]

3)

According to the given data the heat that flows is 133 kilo-joule in quantity.

Answer:

[tex]g \approx 7.4 m/s^2[/tex]

Explanation:

Assuming the following data:

Heigth (m): 0 , 1, 2, 3, 4, 5

Time (s): 0.00, 0.54,0.73, 0.91, 1.01, 1.17

We know from kinematics that the height is given by the following expression:

[tex] h_f = h_i + v_i t + \frac{1}{2} g t^2[/tex]

Assuming for this case that the initial velocity is [tex]v_i[/tex] we can find a polynomial with degree 2 in order to have an estimation for the height with the time.

We can use excel for this and we can see the polynomial adjusted for the data given.

As we can see the best polynomial of degree 2 is given by:

[tex] h(x)= -0.0178 +0.066 x+ 3.6801 x^2[/tex]

For our case x = time and we can rewrite the expression like this

[tex] h(t)= -0.0178 +0.066 t+ 3.6801 t^2[/tex]

And if we are interested on the gravity we want on special the last term of this equation, we can set equal the following terms:

[tex] 3.6801 t^2 = \frac{1}{2} g t^2[/tex]

And solving for g we got:

[tex] 2*3.6801 = g= 7.36 \frac{m}{s^2}[/tex]

So then a good approximation for the gravity of the planet rounded to 2 significant figures is 7.4 m/s^2

To determine the free-fall acceleration on Planet X, you can use the formula: acceleration = 2 * height / fall time^2. Calculating the acceleration for each data point, and the uncertainty can be determined by finding the range of values.

a.

To determine the free-fall acceleration on Planet X, we can use the formula: acceleration = 2 * height / fall time^2. We can calculate the acceleration using the given data:

For height 1m, fall time 0.54s, the acceleration is 7.485 m/s^2

For height 2m, fall time 0.72s, the acceleration is 8.660 m/s^2

For height 3m, fall time 0.91s, the acceleration is 9.337 m/s^2

For height 4m, fall time 1.01s, the acceleration is 9.704 m/s^2

For height 5m, fall time 1.17s, the acceleration is 9.335 m/s^2

b.

To determine the uncertainty in the free-fall acceleration, we can calculate the range of values by subtracting the smallest acceleration from the largest acceleration. The smallest acceleration is 7.485 m/s^2 and the largest acceleration is 9.704 m/s^2. Therefore, the uncertainty in the free-fall acceleration is 2.219 m/s^2.

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Answer:

Explanation:

If you ignore air resistant, then nothing affects the package horizontal motion. In Newton's first law it would keep the package at a constant speed, the speed of the airplane.

So to the eyes of the pilot who is also moving at the same horizontal speed, the lateral position of the package does not change. He can only perceive that the package is getting further away from him as it's dropping vertically.

To a person on the ground then the package is travelling in a parabolic path, where its horizontal speed is constant but vertical speed is increasing toward the ground at the rate of g.

The package would follow a straight line for the pilot and a parabolic curve for an observer on the ground.

The path of the package as observed by the pilot would be a straight line parallel to the airplane's motion. This is because the package falls with the same horizontal velocity as the airplane due to the absence of air resistance. As observed by a person on the ground, the path of the package would be a parabolic curve. This is because the package has an initial horizontal velocity but is acted upon by the force of gravity, causing it to follow a curved trajectory.

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Answer:

They cannot be equal

Explanation:

Let 2 vector equal in magnitude and opposite direction. One of them is 1 and the other is -1

The sum of their magnitudes is 1 + 1 = 2

The magnitude of their sum of 2 vector is 0 since the 2 are in opposite directions, they cancel out each other and their final magnitude is thus 0.

So the sum of the magnitudes of two vectors cannot be equal to the magnitude of the sum of the same two vectors.

An average adult of weigh 70 kg has approximately [tex]7.0 \times 10^{27}[/tex].

Explanation:

Estimation of Atoms in Human Body

We generally evaluate the amount of elements, liquid, or solid bones in a human body but, we can relate these counts to the atomic level as well. Talking about the approximate amount of Hydrogen, Oxygen and Carbon that we carry in our body, they all make 99% of it neglecting 1% of trace elements.

On the basis of this calculation, we can say that a human body of weight 70 kg has around [tex]7.0 \times 10^{27}[/tex] atoms that are differentiated as 2/3 of hydrogen atoms, 1/4 of Oxygen and only 1/3 of Carbon atoms in the total count.

Answer:

So after stretching new resistance will be 0.1823 ohm

Explanation:

We have given initially length of the wire [tex]l_1=150m[/tex]

Radius of the wire [tex]r_1=0.32mm=0.32\times 10^{-3}m[/tex]

Resistance of the wire initially [tex]R_1=90ohm[/tex]

We know that resistance is equal to [tex]R=\frac{\rho l}{A}[/tex] ,here [tex]\rho[/tex] is resistivity, l is length and A is area

From the relation we can say that [tex]\frac{R_1}{R_2}=\frac{l_1}{l_2}\times \frac{A_2}{A_1}[/tex]

Now length of wire become 6.75 m

Volume will be constant

So [tex]A_1l_1=A_2l_2[/tex]

So [tex]\pi \times (0.32)^2\times150=\pi \times r_2^2\times 6.75[/tex]

[tex]r_2=1.508mm[/tex]

So [tex]\frac{90}{R_2}=\frac{150}{6.75}\times \frac{1.508^2}{0.32^2}[/tex]

[tex]R_2=0.1823ohm[/tex]

With the new length and cross-sectional area, we determine the new resistance to be approximately 1822.5 Ohms.

To determine the resistance of the wire after it is stretched, follow these steps:

Calculate the initial volume of the wire using the initial length and cross-sectional area.

The initial length (L1) = 1.50 m

The radius (r1) = 0.32 mm = 0.00032 m

Initial cross-sectional area (A1) = πr1² = π (0.00032 m)² = 3.216 × 10⁻⁷ m²

Initial volume (V) = A1 × L1 = 3.216 × 10⁻⁷ m² × 1.50 m = 4.824 × 10⁻⁷ m³

Since volume remains constant, calculate the new radius after stretching.

The new length (L2) = 6.75 m

Initial volume (V) = New volume (V)

V = A2 × L2; thus, A2 = V / L2 = 4.824 × 10⁻⁷ m³ / 6.75 m = 7.148 × 10⁻⁸ m²

New radius (r2) = √(A2 / π) = √(7.148 × 10⁻⁸ m² / π) ≈ 0.000151 m = 0.151 mm

Calculate the new resistance using the resistivity formula.

Resistance (R) = ρ × L / A

Assuming resistivity (ρ) is the same, R1 / R2 = (L1 / A1) / (L2 / A2)

New resistance (R2) = R1 × (L2 / L1)² = 90 Ω × (6.75 m / 1.50 m)²

R2 = 90 Ω × (4.5)² = 90 Ω × 20.25 ≈ 1822.5 Ω

Therefore, the resistance of the wire after stretching is approximately 1822.5 Ohms.

Answer:

The question is incomplete,below is the complete question

"Calculate the number of atoms contained in a cylinder (1μm radius and 1μm deep)of (a) magnesium (b) lead."

Answer:

a. 1.35*10^{11} atoms

b. 1.03*10^{11} atoms

Explanation:

First, we determine the volume of the magnesium in the cylinder container

using the volume of a cylinder

[tex]V=\pi r^{2}h\\ r=10^{-6}m\\ h=10^{-6}m\\V=\pi *10^{-6*2}*10^{-6}\\V=\pi *10^{-18}\\V=3.14*10^{-18}m^{3}\\[/tex]

a. Next we determine the mass of the magnesium ,

using the density=mass/volume

since density of a magnesium

[tex]the density of magnesium =1.738*10^{3}kg/m^{3} \\mass=density * volume \\mass=1.738*10^{3}*3.14*10^{-18}\\mass=5.46*10^{-15}kg\\ \\mass=5.46*10^{-12}g\\[/tex]

Finally to calculate the number of atoms,

we determine the number of moles

mole=mass/molarmass

[tex]mole=5.46*10^{-12}/ 24.305\\mole=0.225*10^{-12}mol\\[/tex]

Hence the number of atoms is

number of atoms=mole*Avogadro's constant

[tex]number of atoms = 0.225*10^{-12}*6.02*10^{23}\\number of atoms =1.35*10^{11} atoms[/tex]

b. for he lead, we determine the mass of the lead  ,

using the density=mass/volume

since density of a magnesium

[tex]the density of lead =11.34*10^{3}kg/m^{3} \\mass=density * volume \\mass=11.34*10^{3}*3.14*10^{-18}\\mass=35.60*10^{-15}kg\\ \\mass=35.60*10^{-12}g\\[/tex]

Finally to calculate the number of atoms,

we determine the number of moles

mole=mass/molarmass

[tex]mole=35.60*10^{-12}/ 207.2\\mole=0.1718*10^{-12}mol\\[/tex]

Hence the number of atoms is

number of atoms=mole*Avogadro's constant

[tex]number of atoms = 0.1718*10^{-12}*6.02*10^{23}\\number of atoms =1.03*10^{11} atoms[/tex]

Answer

given,

vertical speed of stone,v = 12 m/s

height of the cliff = 70 m

a) time taken by the stone to reach at the bottom of the cliff

We know that,

S = u t + 1/2 a t²

- 70 = 12 t - 0.5 x 9.8 t²

4.9 t² - 12 t - 70 = 0  

solving the equation

t = 5.2 s (neglecting the negative value)

b) again using equation of motion

   v = u + a t

   v = 12 - 9.8 x 5.2

  v = -38.96 m/s

ignoring the negative sign

magnitude of velocity is equal to 38.96 m/s

c) total distance travel by the stone

  vertical distance covered by the stone

 v² = u² + 2 g h

 0 = 12² - 2 x 9.8 x h

 h = 7.34 m

to reach the stone to the same level distance travel be doubled.

Total distance travel by the stone

H = h + h + 70

H = 7.34 x 2 + 70

H = 84.7 m.

Using the equations of motion, we calculated that the stone hits the ground approximately 7.44 seconds after being thrown. The speed at impact would be approximately 36.46 m/s, and the stone would travel a total distance of about 138 meters.

To solve this question, we need to use the equations of motion which are concepts of Physics.

(a) The time it takes for the stone to reach the bottom can be found using the equation: h = ut + 0.5gt², where h is the height =70m, u is the initial velocity =12 m/s, g is the acceleration due to gravity ~= 9.8 m/s², and t is the time we need to find. Solving for 't' gives us approximately 3.72 seconds for the upward journey. The total time taken is twice this value (since the return journey takes the same amount of time), so the stone hits the bottom after approximately 7.44 seconds.

(b) The speed at impact can be calculated using the equation of motion v = u + gt. Using the initial speed u when the stone starts falling from the top = 0, g = 9.8 m/s², and t ~=3.72 seconds, we find the speed is approximately 36.46 m/s.

(c) The total distance traveled can be calculated as the sum of the upward journey (the maximum height the stone reached, which can be calculated using the equation h = ut + 0.5gt² where u = 12m/s, g = 9.8 m/s² and t = ~3.72 seconds) and the downward journey (the fall from the cliff, which is 70m). This gives us an approximate total distance of 70 m + 68 m = 138 m.

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To solve this problem we will apply the concepts related to the kinematic equations of linear motion. Punctually we will verify the vertical displacement and the horizontal displacement from their respective components. We will start by calculating the time it took to reach the objective and later with that time, we will find the horizontal velocity launch component. The position can be written as,

[tex]h= v_{0y}t+\frac{1}{2}a_yt^2[/tex]

Here,

h = Height

[tex]v_{0y}[/tex]= Initial velocity in vertical direction

[tex]a_{y}[/tex] = Vertical acceleration (At this case, due to gravity)

[tex]t[/tex] = Time

There is not vertical velocity because the ball was thrown horizontally), then we have that

[tex]6= (0)t+\frac{1}{2}(9.8)t^2[/tex]

[tex]t = 1.1065s[/tex]

Now using the equation of horizontal motion we have with this time that the initial velocity was,

[tex]x = v_{ox}t+\frac{1}{2}a_xt^2[/tex]

Here,

[tex]v_{0x}[/tex]= Horizontal initial velocity

[tex]t[/tex] = Time

[tex]a_x[/tex] = Acceleration in horizontal plane

There is not acceleration in horizontal plane, only in vertical plane, then we have

[tex]25= v_{0x}(1.1065)+\frac{1}{2}(0)(1.1065)^2[/tex]

[tex]v_{0x} = 22.5938m/s[/tex]

Therefore the pitching speed is 22.5938m/s

The frequency of the loop is 58 Hz and the amplitude of the emf induced in the loop is 7.73 mV and this can be determined by using the given data.

Given :

A stiff wire bent into a semicircle of radius 'a' is rotated with a frequency f in a uniform magnetic field.

According to the data, the angular speed is 58 rev/sec that is, 364.4 rad/sec, the magnetic field is 15 mT that is, 15 [tex]\times[/tex] [tex]10^{-3}[/tex] T, and the radius 'a' is 3 cm that is, 3  [tex]\times[/tex] [tex]10^{-2}[/tex] m.

a) The frequency is 58 rev/sec that is 58 Hz.

b) The amplitude of the emf induced in the loop can be calculated as:

[tex]\rm \epsilon = \dfrac{\omega B \pi a^2}{2}[/tex]

Now, substitute the values of the known terms in the above formula.

[tex]\epsilon = \dfrac{364.4\times 15\times10^{-3}\times \pi \times (3\times 10^{-2})^2}{2}[/tex]

Further, simplify the above expression.

[tex]\rm \epsilon = 0.007728\;V[/tex]

[tex]\rm \epsilon = 7.73\;mV[/tex]

For more information, refer to the link given below:

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