1) An experimental time-travel machine is capable of reaching speeds of 2.992 10⁸ m/s. If the machine travels for 4.42 minutes relative to itself, how long would it have travelled relative to an observer at rest?

use 2.998 10⁸ m/s for the speed of light.

2) A space probe zooms past a planet at 0.78c. An alien who observes the probe moving past measures its length to be 50 m. What is the probes length in its frame of reference?

3) Assume it was possible for an asteroid with a rest mass (9.520x10^20) kg to be travelling through the universe with no particular orbit at a velocity of (1.66x10^8) m/s. What is the relativistic mass of this asteroid?

4) A spaceship travelling at 0.837cflies past a planetoid with a major diameter of 959 km and a minor diameter of 269 km. The spaceship is travelling parallel to the minor diameter. Which diameter of the planet would experience length contraction and what length would an astronaut on the spaceship measure this diameter to be?