More Relativity Problems

1) You are inside your spaceship, floating deep in space, when an alien ship flies past you. (Or do you fly past them?) When their ship is alongside yours, you measure the length of their ship to be exactly as long as yours. Would the aliens measure their own ship to be longer, shorter, or the same length as yours?

2) If a meter stick passed you at 0.25c how long would you measure it to be?

3) A spaceship flies by at 0.850c. You measure its length to be 625 m. How long would the cosmonauts on board the ship measure it to be?

4) A sailboat passes by as you sit by a lake. The folks on the boat measure its length to be 10.0 m, but you measure the boat to be 7.50 m in length. How fast do you think the boat is moving?

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

6) You’re driving along at truly unreasonable 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.)

7) How fast would a car need to move before its mass is seen to increase from 1280 kg to 2250 kg?

8) The swallow is a type of bird not known for flying at relativistic speeds. However, let’s assume a swallow flies past you with an airspeed of 0.9999c. You measure it to have a mass of 3010 g while moving. What is the mass of the bird at rest?

9)
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?

10) It is not possible for something other than light to move at the speed of light! There is a reason for this, and it’s not difficult to understand. Assume a person’s rest mass is 75 kg. Calculate their mass if they were moving at the speed of light, as measured by an observer at rest.