Question

An enemy spaceship is moving toward your starfighter with a speed, as measured in your frame, of 0.400c. The enemy ship fires a missile toward you at a speed of 0.700c 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. (b) If you measure that the enemy ship is 8.00×106km away from you when the missile is fired, how much time, measured in your frame, will it take the missile to reach you

Answer 1

Answer:

0.859375c

31.03 seconds

Explanation:

v' = Velocity of my ship = 0.4 c

u = Velocity of rocket = 0.7 c

c = Speed of light = $3\times 10^8\ m/s$

s = Distance between my ship and enemy ship = $8\times 10^6\ km$

Relativistic addition of speed is given by

$v=\dfrac{v'+u}{1+\dfrac{uv'}{c^2}}\\\Rightarrow v=\dfrac{0.7+0.4}{1+\dfrac{0.7c\times 0.4c}{c^2}}\\\Rightarrow v=0.859375\ c$

The speed of the missile is 0.859375c

Time is given by

$t=\dfrac{s}{v}\\\Rightarrow t=\dfrac{8\times 10^9}{0.859375\times 3\times 10^8}\\\Rightarrow t=31.03\ s$

It will take 31.03 seconds to reach me.