The Andromeda galaxy is 2 million light years away from the Milky Way. although nothing can go faster than the speed of light, it would still be possible to travel to AndroMeda in much less than 2 million years. How?

The Lorentz contraction formula in relativity theory relates the length L of an object moving at a velocity of v mi/sec with respect to an ob- server to its length Lo at rest. If c is the speed of light, then L2 = Lo2 (1- v2 / c2) For what velocities will L be less than L.? State the answer in terms of c.

The spaceship Lilac, based on the Purple Planet, is 711 m long when measured at rest. When the Lilac passes Earth, observers there measure its length to be 655 m. At what speed ? is the Lilac moving with respect to Earth? Express your answer as a multiple of the speed of light ?.

Setup: A futuristic race from Earth to Alpha Centauri is taking place. But the winner of the race isn't who gets there first, it's who measures the smallest proper time along the way. The competitors start on Earth, from position (t, x) = (0, 0). They must travel from Earth (considered stationary) to Alpha Centauri, a distance of L = 4.37 light years away, such that they arrive at Alpha Centauri at Earth time of T = 10 years. Upon arrival, they compare their personal times (the proper time they measure along their whole trip) and the team with the smallest proper time wins. Question: a) Team A's spaceship immediately blasts off at (t, x) = (0, 0) and travels at a constant speed until they reach Alpha Centauri at Earth time of 10 years. Team B, on the other hand, have a much faster ship— they can travel so fast, you may consider their maximum speed to be the speed of light. Team B stays stationary on Earth for as long as they can; then, they blast off and travel at constant maximum…