A rocket ship flies past the earth at 87.0 % of the speed of light. Inside, an astronaut who is undergoing a physical examination is having his height measured while he is lying down parallel to the direction the rocket ship is moving.

If his height is measured to be 1.96 m by his doctor inside the ship, what height would a person watching this from earth measure for his height?

0.967m

Explanation:

Rocket's speed = 0.87c

Where c is speed of light in space

Since he's lying vertical his height becomes a length

Lenght l' = Lenght in rocket = 1.96m

Percieved Lenght on earth l =?

Due to relativistic effect his length will be reduced to;

l = l'(1-(v/c)^2)^0.5

l = 1.96(1-0.87^2)^0.5

l = 1.96(1-0.7569)^0.5

l = 1.96(0.2431)^0.5

l = 1.96(0.4931) = 0.967m

365.25 earth days are in the year of a light year