A rocket ship flies past the earth at 77.0 % of the speed of light. Inside, an a
ID: 1333043 • Letter: A
Question
A rocket ship flies past the earth at 77.0 % 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.
1: If his height is measured to be 1.90 m by his doctor inside the ship, what height would a person watching this from earth measure for his height?
2: If the earth-based person had measured 1.90 m , what would the doctor in the spaceship have measured for the astronaut's height?
3: Is this a reasonable height?
Avaliable options (Yes or No).
4: 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: What would the observer on earth measure for his height now?
Explanation / Answer
given,
speed of the ship = 0.77c
height measured in ship = 1.9 m
L = Lo * sqrt(1 - v^2 / c^2)
L = 1.9 * sqrt(1 - 0.77^2)
L = 1.212 m
height of the person observed from earth = 1.212 m
1.9 = Lo * sqrt(1 - 0.77^2)
Lo = 2.9778 m
height of the person observed by the doctor = 2.9778 m
if the person gets up the height will remain unchanged and the doctor will observe the same height that is 1.9 m
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