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

Question

Want to see more full solutions like this?

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.

Want to see more full solutions like this?

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

Students have asked these similar questions

suggest a reason ultrasound cleaning is better than cleaning by hand?

Checkpoint 4 The figure shows four orientations of an electric di- pole in an external electric field. Rank the orienta- tions according to (a) the magnitude of the torque on the dipole and (b) the potential energy of the di- pole, greatest first. (1) (2) E (4)

What is integrated science. What is fractional distillation What is simple distillation

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.

Want to see more full solutions like this?

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

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.

Want to see more full solutions like this?

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

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.

Want to see more full solutions like this?

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.