The speed of the payload (fired by a rocket)relative to earth

Question

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Answer 1

Question

Chapter 26, Problem 1OQ

To determine

The speed of the payload (fired by a rocket)relative to earth

Expert Solution & Answer

Answer to Problem 1OQ

Solution:

Option d: A little under c, is the correct answer.

Explanation of Solution

Given:

A rocket headed away from the earth with the speed of 0.80 c and it fires a small payload at a speed of 0.70 c (relative to rocket).

The speed of the rocket relative to earth v = 0.80 c

The velocity of the payload fired by the rocket u₁ = 0.70 c

The speed of the light c = 3×10⁸ m/s

Formula used:

The speed of the payload relative to earth u =?

Einstein’s relativistic formula

$u = \frac{v + u_{1}}{1 + \frac{v u_{1}}{c^{2}}}$

Where,

$v is the speed of the rocket$

$u_{1} is the speed of the payload relative to rocket$

Calculation:

The speed of the payload relative to earth can be found from the equation

$u = \frac{(0.80 c + 0.70 c)}{(1 + \frac{0.80 c \times 0.70 c}{c^{2}})}$

$u = \frac{1.5 c}{1 + \frac{0.56 c^{2}}{c^{2}}}$

$\begin{array}{l} u = \frac{1.5 c}{1.56} \\ u = 0.96 c \end{array}$

Analysis of options:

Option a: 1.50c

Option b: A little less than 1.50 c

Option c: A little over c

All the above three options are wrong, because, no object can travel faster than the speed of light in any reference frame. All the above options describe that the speeds are greater than c which is impossible. So, all are wrong.

Option d: A little under c

The velocity of the payload has been calculated as 0.96 c. Hence, it is the correct answer.

Option e: 0.75 c

As the velocity of the pay load is found to be 0.96 c.This is a wrong answer.

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I. Pushing on a File Cabinet Bob has been asked to push a heavy file cabinet down the hall to another office. It's not on rollers, so there is a lot of friction. At time t = 0 seconds, he starts pushing it from rest with increasing force until it starts to move at t = 2 seconds. He pushes the file cabinet down the hall with varying amounts of force. The velocity versus time graph of the cabinet is shown below. A. On the graphs provided below, 1. draw the net force vs. time that would produce this velocity graph; 2. draw the friction force vs. time for this motion; 3. draw the applied force (Fon Cabinet by Bob) VS. time for this motion (the first two seconds of this graph have been drawn for you). Velocity (m/s) Applied Force (N) Friction Force (N) Net Force (N) A -m B -U time (s) D time (s) time (s) time (s)

answer it

Please draw a sketch and a FBD

Answer 2

Question

Chapter 26, Problem 1OQ

To determine

The speed of the payload (fired by a rocket)relative to earth

Expert Solution & Answer

Answer to Problem 1OQ

Solution:

Option d: A little under c, is the correct answer.

Explanation of Solution

Given:

A rocket headed away from the earth with the speed of 0.80 c and it fires a small payload at a speed of 0.70 c (relative to rocket).

The speed of the rocket relative to earth v = 0.80 c

The velocity of the payload fired by the rocket u₁ = 0.70 c

The speed of the light c = 3×10⁸ m/s

Formula used:

The speed of the payload relative to earth u =?

Einstein’s relativistic formula

$u = \frac{v + u_{1}}{1 + \frac{v u_{1}}{c^{2}}}$

Where,

$v is the speed of the rocket$

$u_{1} is the speed of the payload relative to rocket$

Calculation:

The speed of the payload relative to earth can be found from the equation

$u = \frac{(0.80 c + 0.70 c)}{(1 + \frac{0.80 c \times 0.70 c}{c^{2}})}$

$u = \frac{1.5 c}{1 + \frac{0.56 c^{2}}{c^{2}}}$

$\begin{array}{l} u = \frac{1.5 c}{1.56} \\ u = 0.96 c \end{array}$

Analysis of options:

Option a: 1.50c

Option b: A little less than 1.50 c

Option c: A little over c

All the above three options are wrong, because, no object can travel faster than the speed of light in any reference frame. All the above options describe that the speeds are greater than c which is impossible. So, all are wrong.

Option d: A little under c

The velocity of the payload has been calculated as 0.96 c. Hence, it is the correct answer.

Option e: 0.75 c

As the velocity of the pay load is found to be 0.96 c.This is a wrong answer.

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Answer 3

Question

Chapter 26, Problem 1OQ

To determine

The speed of the payload (fired by a rocket)relative to earth

Expert Solution & Answer

Answer to Problem 1OQ

Solution:

Option d: A little under c, is the correct answer.

Explanation of Solution

Given:

A rocket headed away from the earth with the speed of 0.80 c and it fires a small payload at a speed of 0.70 c (relative to rocket).

The speed of the rocket relative to earth v = 0.80 c

The velocity of the payload fired by the rocket u₁ = 0.70 c

The speed of the light c = 3×10⁸ m/s

Formula used:

The speed of the payload relative to earth u =?

Einstein’s relativistic formula

$u = \frac{v + u_{1}}{1 + \frac{v u_{1}}{c^{2}}}$

Where,

$v is the speed of the rocket$

$u_{1} is the speed of the payload relative to rocket$

Calculation:

The speed of the payload relative to earth can be found from the equation

$u = \frac{(0.80 c + 0.70 c)}{(1 + \frac{0.80 c \times 0.70 c}{c^{2}})}$

$u = \frac{1.5 c}{1 + \frac{0.56 c^{2}}{c^{2}}}$

$\begin{array}{l} u = \frac{1.5 c}{1.56} \\ u = 0.96 c \end{array}$

Analysis of options:

Option a: 1.50c

Option b: A little less than 1.50 c

Option c: A little over c

All the above three options are wrong, because, no object can travel faster than the speed of light in any reference frame. All the above options describe that the speeds are greater than c which is impossible. So, all are wrong.

Option d: A little under c

The velocity of the payload has been calculated as 0.96 c. Hence, it is the correct answer.

Option e: 0.75 c

As the velocity of the pay load is found to be 0.96 c.This is a wrong answer.

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Answer 4

Question

Chapter 26, Problem 1OQ

To determine

The speed of the payload (fired by a rocket)relative to earth

Expert Solution & Answer

Answer to Problem 1OQ

Solution:

Option d: A little under c, is the correct answer.

Explanation of Solution

Given:

A rocket headed away from the earth with the speed of 0.80 c and it fires a small payload at a speed of 0.70 c (relative to rocket).

The speed of the rocket relative to earth v = 0.80 c

The velocity of the payload fired by the rocket u₁ = 0.70 c

The speed of the light c = 3×10⁸ m/s

Formula used:

The speed of the payload relative to earth u =?

Einstein’s relativistic formula

$u = \frac{v + u_{1}}{1 + \frac{v u_{1}}{c^{2}}}$

Where,

$v is the speed of the rocket$

$u_{1} is the speed of the payload relative to rocket$

Calculation:

The speed of the payload relative to earth can be found from the equation

$u = \frac{(0.80 c + 0.70 c)}{(1 + \frac{0.80 c \times 0.70 c}{c^{2}})}$

$u = \frac{1.5 c}{1 + \frac{0.56 c^{2}}{c^{2}}}$

$\begin{array}{l} u = \frac{1.5 c}{1.56} \\ u = 0.96 c \end{array}$

Analysis of options:

Option a: 1.50c

Option b: A little less than 1.50 c

Option c: A little over c

All the above three options are wrong, because, no object can travel faster than the speed of light in any reference frame. All the above options describe that the speeds are greater than c which is impossible. So, all are wrong.

Option d: A little under c

The velocity of the payload has been calculated as 0.96 c. Hence, it is the correct answer.

Option e: 0.75 c

As the velocity of the pay load is found to be 0.96 c.This is a wrong answer.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 26, Problem 1OQ

To determine

The speed of the payload (fired by a rocket)relative to earth

Expert Solution & Answer

Answer to Problem 1OQ

Solution:

Option d: A little under c, is the correct answer.

Explanation of Solution

Given:

A rocket headed away from the earth with the speed of 0.80 c and it fires a small payload at a speed of 0.70 c (relative to rocket).

The speed of the rocket relative to earth v = 0.80 c

The velocity of the payload fired by the rocket u₁ = 0.70 c

The speed of the light c = 3×10⁸ m/s

Formula used:

The speed of the payload relative to earth u =?

Einstein’s relativistic formula

$u = \frac{v + u_{1}}{1 + \frac{v u_{1}}{c^{2}}}$

Where,

$v is the speed of the rocket$

$u_{1} is the speed of the payload relative to rocket$

Calculation:

The speed of the payload relative to earth can be found from the equation

$u = \frac{(0.80 c + 0.70 c)}{(1 + \frac{0.80 c \times 0.70 c}{c^{2}})}$

$u = \frac{1.5 c}{1 + \frac{0.56 c^{2}}{c^{2}}}$

$\begin{array}{l} u = \frac{1.5 c}{1.56} \\ u = 0.96 c \end{array}$

Analysis of options:

Option a: 1.50c

Option b: A little less than 1.50 c

Option c: A little over c

All the above three options are wrong, because, no object can travel faster than the speed of light in any reference frame. All the above options describe that the speeds are greater than c which is impossible. So, all are wrong.

Option d: A little under c

The velocity of the payload has been calculated as 0.96 c. Hence, it is the correct answer.

Option e: 0.75 c

As the velocity of the pay load is found to be 0.96 c.This is a wrong answer.

Answer 6

Chapter 26, Problem 1OQ

To determine

The speed of the payload (fired by a rocket)relative to earth

Expert Solution & Answer

Answer to Problem 1OQ

Solution:

Option d: A little under c, is the correct answer.

Explanation of Solution

Given:

A rocket headed away from the earth with the speed of 0.80 c and it fires a small payload at a speed of 0.70 c (relative to rocket).

The speed of the rocket relative to earth v = 0.80 c

The velocity of the payload fired by the rocket u₁ = 0.70 c

The speed of the light c = 3×10⁸ m/s

Formula used:

The speed of the payload relative to earth u =?

Einstein’s relativistic formula

$u = \frac{v + u_{1}}{1 + \frac{v u_{1}}{c^{2}}}$

Where,

$v is the speed of the rocket$

$u_{1} is the speed of the payload relative to rocket$

Calculation:

The speed of the payload relative to earth can be found from the equation

$u = \frac{(0.80 c + 0.70 c)}{(1 + \frac{0.80 c \times 0.70 c}{c^{2}})}$

$u = \frac{1.5 c}{1 + \frac{0.56 c^{2}}{c^{2}}}$

$\begin{array}{l} u = \frac{1.5 c}{1.56} \\ u = 0.96 c \end{array}$

Analysis of options:

Option a: 1.50c

Option b: A little less than 1.50 c

Option c: A little over c

All the above three options are wrong, because, no object can travel faster than the speed of light in any reference frame. All the above options describe that the speeds are greater than c which is impossible. So, all are wrong.

Option d: A little under c

The velocity of the payload has been calculated as 0.96 c. Hence, it is the correct answer.

Option e: 0.75 c

As the velocity of the pay load is found to be 0.96 c.This is a wrong answer.

Answer 7

Chapter 26, Problem 1OQ

To determine

The speed of the payload (fired by a rocket)relative to earth

Answer 8

Expert Solution & Answer

Answer to Problem 1OQ

Solution:

Option d: A little under c, is the correct answer.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Given:

A rocket headed away from the earth with the speed of 0.80 c and it fires a small payload at a speed of 0.70 c (relative to rocket).

The speed of the rocket relative to earth v = 0.80 c

The velocity of the payload fired by the rocket u₁ = 0.70 c

The speed of the light c = 3×10⁸ m/s

Formula used:

The speed of the payload relative to earth u =?

Einstein’s relativistic formula

$u = \frac{v + u_{1}}{1 + \frac{v u_{1}}{c^{2}}}$

Where,

$v is the speed of the rocket$

$u_{1} is the speed of the payload relative to rocket$

Calculation:

The speed of the payload relative to earth can be found from the equation

$u = \frac{(0.80 c + 0.70 c)}{(1 + \frac{0.80 c \times 0.70 c}{c^{2}})}$

$u = \frac{1.5 c}{1 + \frac{0.56 c^{2}}{c^{2}}}$

$\begin{array}{l} u = \frac{1.5 c}{1.56} \\ u = 0.96 c \end{array}$

Analysis of options:

Option a: 1.50c

Option b: A little less than 1.50 c

Option c: A little over c

All the above three options are wrong, because, no object can travel faster than the speed of light in any reference frame. All the above options describe that the speeds are greater than c which is impossible. So, all are wrong.

Option d: A little under c

The velocity of the payload has been calculated as 0.96 c. Hence, it is the correct answer.

Option e: 0.75 c

As the velocity of the pay load is found to be 0.96 c.This is a wrong answer.