Question

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?

Answer 1

L=0.9664m

Step-by-step explanation:

According to length the astronaut with respect to a person watching from earth is:

`L = L_p=\sqrt{1-(v^2)/(c^2) }`

Given that,

87.0 % of the speed of light, v

height is measured to be 1.96 m,Lp

substitute the values in the equation

`L = L_p=\sqrt{1-(v^2)/(c^2) }`

`L = (1.96)√(1-0.87^2)`

`L = (1.96)√(1 -0.7569)`

`L =(1.96)√(0.2431)`

`L = (1.96)*0.4931`

`L=0.9664m`

Answer 2

Answer: 0.967m

Step-by-step 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