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 × 10^{8}
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 (½mv^{2})
for a particle moving at a speed of 0.975c.