A rocket ship flies past the earth at 89.0 % of the speed of light. Inside, an a

Question

A rocket ship flies past the earth at 89.0 % 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.
a) If his height is measured to be 1.95 m by his doctor inside the ship, what height would a person watching this from earth measure for his height?
b)Suppose the astronaut in part (a) gets up after the examination and stands with his body perpendicular to the direction of motion. What would the doctor in the rocket measure for his height now?

5 star for correct answer, thank you in advance :)

Explanation / Answer

length contraction occurs only along the direction of motion.

so when an object is moving with veloicty v (where v is close to speed of light), length as measured from a fixed source , let be L0.

then length as measured from a fixe referrence frame=L=L0*sqrt(1-(v/c)^2)

a)v=0.89*c

L0=1.95 m

then L=1.95*sqrt(1-(0.89*c/c)^2)

=0.889 m

b)as his height is now perpendicular to direction of motion, there wont be any contraction.

so his height will still be observed as 1.95 m.

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