Chapter 37: 30P (page 1147)

Stellar system Q₁ moves away from us at a speed of 0.800c. Stellar system Q₂, which lies in the same direction in space but is closer to us, moves away from us at speed 0.400c. What multiple of c gives the speed of Q₂ as measured by an observer in the reference frame of Q₁?

Short Answer

Expert verified

The multiple of c is 0.588.

Step by step solution

Describe the expression for the velocity of the particle

The relativistic velocity of the particle is given by,

$u = \frac{u^{'} + v}{1 + \frac{u^{'} v}{c}}$ …… (1)

Here, data-custom-editor="chemistry" $u = 0.400 c$ is the velocity of stellar Q₂ in reference frame, and data-custom-editor="chemistry" $u = 0.800 c$ is the velocity of the reference frame of the observer on stellar Q₁ relative to the reference frame.

Determine the multiple of c

Rearrange the equation (1) for u^'.

$\begin{array}{rcl} u (1 + \frac{u^{'} v}{c^{2}}) & = & u^{'} + v \\ \frac{{uu}^{'} v}{c} - u^{'} & = & v - u \\ u^{'} (\frac{uv}{c^{2}} - 1) & = & v - u \\ u^{'} & = & \frac{v - u}{(\frac{uv}{c^{2}} - 1)} \end{array}$ …… (2)

Substitute 0.800c for v, and 0.400c for u in equation (2).

$\begin{array}{rcl} u^{'} & = & \frac{0.800 c - 0.400 c}{\frac{(0.800 c) (0.400 c)}{c^{2}} - 1} \\ = & \frac{0.400 c}{0.32 - 1} \\ = & - 0.588 c \end{array}$

Here, the negative sign indicates the opposite direction.

Therefore, the multiple of c is 0.588.

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Stellar system Q₁ moves away from us at a speed of 0.800c. Stellar system Q₂, which lies in the same direction in space but is closer to us, moves away from us at speed 0.400c. What multiple of c gives the speed of Q₂ as measured by an observer in the reference frame of Q₁?

Short Answer

Step by step solution

Describe the expression for the velocity of the particle

Determine the multiple of c

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Stellar system Q1 moves away from us at a speed of 0.800c. Stellar system Q2, which lies in the same direction in space but is closer to us, moves away from us at speed 0.400c. What multiple of c gives the speed of Q2 as measured by an observer in the reference frame of Q1?

Short Answer

Step by step solution

Describe the expression for the velocity of the particle

Determine the multiple of c

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fundamentals of Physics

Fields in Physics

Solid State Physics

Electromagnetism

Electrostatics

Circular Motion and Gravitation

Study anywhere. Anytime. Across all devices.

Stellar system Q₁ moves away from us at a speed of 0.800c. Stellar system Q₂, which lies in the same direction in space but is closer to us, moves away from us at speed 0.400c. What multiple of c gives the speed of Q₂ as measured by an observer in the reference frame of Q₁?