1. A spaceship travels at a constant speed from earth to a planet orbiting anoth

Question

1. A spaceship travels at a constant speed from earth to a planet orbiting another star. When the spacecraft arrives, 15 years have elapsed on earth, and 9.9 years have elapsed on board the ship. How far away (in meters) is the planet, according to observers on earth?

2. Starting from rest, two skaters "push off" against each other on smooth level ice, where friction is negligible. One is a woman and one is a man. The woman moves away with a velocity of +2.9 m/s relative to the ice. The mass of the woman is 52 kg, and the mass of the man is 71 kg. Assuming that the speed of light is 4.1 m/s, so that the relativistic momentum must be used, find the recoil velocity of the man relative to the ice.

Explanation / Answer

1. Y = 15 / 9.9 = 1.515

Y = 1 / sqrt[1 - (v/c)^2] = 1.515

v/c = 0.75

v = 0.75c

according to observer on earth,

d = (0.75 x 3 x 10^8) (15 x 365 x 24 x 3600 s)

d = 1.066 x 10^17 m

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