Question

Luke Skywalker is flying his X-wing at 840 m/s down the Death Star trench.
Darth Vader is 320 meters behind him, going 740 m/s.
Luke's ship is going as fast as it can, so its speed isn't changing. Darth Vader's ship is gaining speed at a rate of 20.6 m/s². When Darth Vader gets to within 145 m, he will be close enough to lock on with his targetting system and blow up Luke's ship.

(a) How much time does Luke have to use the Force and launch his torpedoes at the Death Star already?
seconds.


(b) What is the furthest Luke's ship ever gets ahead of the TIE fighter?
m ahead.
_{Pro-tip: for as long as Luke's speed is faster than Vader's, the distance between them continues to increase and hasn't yet reached its maximum value.}

Answer 1

a) Let at t = 0, Vader be at x = 0

His position at a time t is given by

Now, luke's position will be

x = 320 m (ahead of Vader)

His constant speed is 840 m/s

So, His position at time t is given by

The difference in their position at any time t is given by

When this becomes equal to 145 m, Vader can fire.

So,

Only the positive solution can be taken.

SO,

b) For as long as Luke's speed is faster than Vader's, the distance between them continues to increase and hasn't yet reached its maximum value.

We have to find the time taken for Vader's speed to be equal to Luke's

Using

v = u + at

t = (v-u)/a = (840-740)/20.6 = 4.854 s

At this time, the separation will be