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.

Part A

If his height is measured to be 1.97 m by his doctor inside the ship, what height would a person watching this from earth measure for his height?

h =

  m  

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Part B

If the earth-based person had measured 1.97 m , what would the doctor in the spaceship have measured for the astronaut's height?

h =

  m  

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Part C

Is this a reasonable height?

Is this a reasonable height?

yes

no

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Part D

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 h

is height now?

hrocket =

  m  

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Part E

What would the observer on earth measure for his height now?

honearth =

  m  

Answer 1

a)

speed = 0.77 C

height L₀ = 1.97 m

L = L₀ ( 1 - v² / c² )^1/2

L = 1.97 X ( 1 - 0.77² )^1/2

L = 1.256 m

b )

1.97 = L₀ ( 1 - v² / c² )^1/2

1.97 = L₀ ( 1 - 0.77² )^1/2

L₀ = 1.97 / ( 1 - 0.77² )^1/2

L₀ = 3.08 m

c )

YES it is the reasonable height

d )

Suppose the astronaut in part (a) gets up after the examination and stands with his body perpendicular to the direction of motion so it is same height 1.97 m

e )

1.97 = L₀ ( 1 - v² / c² )^1/2

1.97 = L₀ ( 1 - 0.77² )^1/2

L₀ = 1.97 / ( 1 - 0.77² )^1/2

L₀ = 3.08 m