An enemy spaceship is moving toward your starfighter with a speed of 0.400c , as

Question

An enemy spaceship is moving toward your starfighter with a speed of 0.400c , as measured in your reference frame. The enemy ship fires a missile toward you at a speed of 0.700c relative to the enemy ship. If you measure the enemy ship to be 1.00 x 107km away from you when the missile is fired, how much time t, measured in your frame, will it take the missile to reach you?(Figure 1)

If the enemy spaceship were to fire the missile with a velocity, relative to the enemy's spaceship, 20% higher than before, how much time will it take the missile to reach you, as measured in your frame?

t = ___________________s

Explanation / Answer

We need the relativistic velocity addition

In this case...

u = -.84c

u' = ?

v = .4c

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

u' = (-.84c - .4c)/(1 - (-.84)(.4))

u' = .9281c

Then d = vt

(1 x 107)(1000) = (.9281)(3 X 108)(t)

t = 35.9 sec

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