Still More Relativity Problems

1)      A tortoise and a rabbit are having a race. The rabbit passes the tortoise at 0.900c, with respect to the tortoise. The tortoise has a speed of 0.300c with respect to the earth. Calculate the speed of the rabbit with respect to the earth.

2)      A relativistic archer fires an arrow from the back of a running horse. The arrow is 125 cm long, and 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?

3)      A cubical box flies past you at 0.855c. A person inside the box measures one of its walls to be 2.50 m by 2.50 m. If you see the box moving parallel to one of its edges, what do you measure to be the area of a wall?

4)      There are two twins on earth. One gets aboard a rocket and leaves the planet at 0.950c. If 1.25 years pass for the twin on the rocket, how much time will the rocket twin say has passed for his twin on earth?

5)      If 1.00 kg flies past you at 275,000,000 m/s what will you measure to be its mass? However, assume the speed of light is infinitely fast and not 3.00 × 108 m/s.

6)      How fast would you need to be moving for your total energy to be exactly twice your rest energy?

7)      Find the ratio of relativistic kinetic energy to non-relativistic kinetic energy (½mv2) for a particle moving at a speed of 0.975c.