Question

SPECIAL RELATIVITY QUESTION
Bob, in frame (x,ct), shoots a missile from Earth at 0.5c, aiming at an asteroid that is approaching Earth at a speed of 0.7c. Bob launches the missile (event A) at t=x=0 when the asteroid is 18 light-years away in (x,ct). A timer on board the missile causes the missile to explode when it reads 10 minutes (event B). The light from the explosion later reaches the asteroid (event C) and the Earth (event D).

Answer 1

a) When and where does Bob measure the missile to explode in (x,ct)?
b) In the frame of the Earth, does the light from the explosion reach the Earth first, or
asteroid first?
c) In the frame of the asteroid, does the light from the explosion reach the Earth first, or
the asteroid first?

Answer 2

I don't feel qualified to answer this, sorry! But I would think that you would want to start by finding the time dilation for the missile. According to Bob, the missile time is dilated, or slowed. With help of Wikipedia, I can say:
\[\Delta t' = \frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}}\]

If you know how much time it took, according to Bob, and you know the velocity, according to Bob, then you can find the distance traveled, according to Bob, right?