An enemy spaceship is moving toward your starfighter with a speed of 0.490c, as

Question

An enemy spaceship is moving toward your starfighter with a speed of 0.490c, as measured in your reference frame. The enemy ship fires a missile toward you at a speed of 0.740c relative to the enemy ship.

a. What is the speed of the missile relative to you? Express your answer in terms of the speed of light.
v = ____________c

b.If you measure the enemy ship to be 8.70 x 106km away from you when the missile is fired, how much time, measured in your frame, will it take the missile to reach you?
t = ____________s

Explanation / Answer

We need the relativistic velocity addition

In this case...

u = -.74c

u' = ?

v = .49c

Apply u' = (u-v)/(1 - uv/c2)

u' = (-.74c - .49c)/(1 - (-.74)(.49))

u' = .9026c

Then d = vt

(8.7 x 106)(1000) = (.9026)(3 X 108)(t)

t = 32.129 sec

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