An enemy is fleeing at .2c relative to your rocketship, so you decide to shoot a
ID: 2050146 • Letter: A
Question
An enemy is fleeing at .2c relative to your rocketship, so you decide to shoot a missile which leaves your ship at .6c relative to you. It also has a fixed timer which says it will detonate in 12 seconds.
1. What is the speed of the enemy relative to the missile?
2. How far ahead must the enemy ship be when you shoot the missile?
3. How far does the missile travel between launch and impact, according to the missile?
4. how much time elapses on the enemy ship between missile launch and impact?
5. how much time passes on the enemy ship between seeing the missile launch and when it actually hits? (how long to react)
How to represent these on a space-time diagram?
Explanation / Answer
1. speed of enemy relative to missile = 0.2c - 0.6c = -0.4c 2. Distance when the missile is shot = 0.4c * 12 = 0.4*3*10^8 * 12 = 1.44*10^9 m 3. Distance traveled by the missile = 0.6c * 12 = 2.16*10^9 m 4.Time elapsed = 12 seconds 5. Velocity of enemy w.r.t. light = 0.2c - c = -0.8c So, time taken for the enemy to see the missile after it is actually launched = 1.44*10^9 / 0.8c = 6 seconds So, time to react = 12-6 = 6 seconds