Question

Imagine Punch lives on the Earth at rest. Judy is traveling past the earth with a speed of 0.600 c. If a rocket moving in the same direction passes Judy, Punch sees the speed of the rocket to be 0.870 c. What is the speed of the rocket seen by Judy in terms of the speed of the light?

Answer 1

Answer:

0.565 c

Explanation:

$v_{J}$ = velocity of judy relative to punch on earth = 0.600 c

$v_{R}$ = velocity of rocket relative to punch on earth = 0.870 c

$v_{RJ}$ = velocity of rocket relative to judy = ?

velocity of rocket relative to judy is given as

$v_{RJ} = \frac{v_{R} - v_{J}}{1 - \frac{v_{R}v_{J}}{c^{2}}}$

inserting the values

$v_{RJ} = \frac{(0.870 c) - (0.600 c)}{1 - \frac{(0.870 c)(0.600 c)}{c^{2}}}$

$v_{RJ} = \frac{0.270 c}{0.478}$

$v_{RJ} = 0.565 c$