Chapter 36: Q. 29 (page 1060)

A rocket cruising past earth at $0.80 c$ shoots a bullet out the back door, opposite the rocket’s motion, at $0.90 c$ relative to the rocket. What is the bullet’s speed, as a fraction of $c$ , relative to the earth?

Short Answer

Expert verified

The bullet’s speed of $- 0.36 c$ is relative to the earth.

Step by step solution

Given Information

We have given that a rocket cruising past earth at $0.80 c$ shoots a bullet out the back door, opposite the rocket’s motion, at $0.90 c$ relative to the rocket. We have to find the bullet’s speed, as a fraction of $c$ , relative to the earth.

Simplify

Assemble the frames as follows:

The $S$ – Frame is the Earth.

The $S'$ – Frame rocket is moving at $0.80 c$ relative to the $S$ – Frame.

The "event" involves firing the bullet out of the rocket in the $S'$ – Frame, in the opposite direction of the rocket's path. According to the $S'$ – Frame, the velocity is $- 0.90 c$ .

Calculate the bullet's speed in relation to the Earth:

$u_{x} = \frac{u_{x}' + v}{1 + \frac{u_{x}' + v}{c^{2}}} = \frac{(- 0.90 c) + (0.80 c)}{1 + \frac{(- 0.90 c) (0.8 c)}{c^{2}}} = - 0.36 c$

Therefore, the bullet’s speed of $- 0.36 c$ is relative to the earth.

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A rocket cruising past earth at $0.80 c$ shoots a bullet out the back door, opposite the rocket’s motion, at $0.90 c$ relative to the rocket. What is the bullet’s speed, as a fraction of $c$ , relative to the earth?

Short Answer

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Given Information

Simplify

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A rocket cruising past earth at 0.80cshoots a bullet out the back door, opposite the rocket’s motion, at 0.90c relative to the rocket. What is the bullet’s speed, as a fraction of c, relative to the earth?

Short Answer

Step by step solution

Given Information

Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Mechanics and Materials

Fields in Physics

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Linear Momentum

Study anywhere. Anytime. Across all devices.

A rocket cruising past earth at $0.80 c$ shoots a bullet out the back door, opposite the rocket’s motion, at $0.90 c$ relative to the rocket. What is the bullet’s speed, as a fraction of $c$ , relative to the earth?