More Relativity Problems

1) You’re driving along at relativistic speeds and you observe two lightning bolts strike your car. One strikes the front of your car and the other strikes the rear. To you it appears that both bolts strike your car at the same time. What would an observer at rest outside your car see? (Assume you’re not driving backwards, which would be reckless.)

2) If you were moving away from a star at half the speed of light (0.5c), at what speed would you see the light from the star pass you?

3) While you are sitting in front of your house, a jogger passes you at 0.98c. If 1.0 minute passes on your watch, how much time passes on hers?

4) A proton at rest has a mass of 1.6726 ´ 10 ^{- 27} kg. What would you measure to be its mass if it were moving at 0.99999c?

5) If an arrow 125 cm long is shot past you at 295,000,000 m/s how long will it appear?

6) How fast would a stick need to move before it is seen to shrink from exactly 100 cm to 37 cm?

7) At what speed does the mass of a moving car differ from the mass of the car at rest by 1.0%?

8) A tortoise and a rabbit are racing past the planet Jupiter. The rabbit passes the tortoise at 0.90c, with respect to the tortoise. The tortoise has a speed of 0.30c with respect to Jupiter. Calculate the speed of the rabbit with respect to Jupiter.

9) A person is approaching you from your left at 0.80c. A second person is approaching you from your right at 0.60c. What is the relative speed of one person with respect to the other?

10) A relativistic archer fires an arrow from a running horse, so that the horse is running in one direction and the arrow is flying in the opposite direction. The arrow, at rest, is 125 cm long. The archer sees the arrow move at 295,000,000 m/s. If you see the horse running at 175,000,000 m/s, how long is the arrow from your perspective?

11) Recall, a proton has a rest mass of 1.6726 ´ 10 ^{- 27} kg. If it were moving at 0.99c what would be (a) its total energy and (b) its kinetic energy?

12) Quasars are thought to be some of the most distant, and possibly the brightest, objects in the universe, and it’s possible that their brightness could be powered by enormous black holes. If a quasar were to emit 10⁴¹ Joules of energy in one second (i.e. 10⁴¹ Watts) how much mass would need to be converted each second to supply the energy?