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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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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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.