Constants PartA You\'re standing on an asteroid when you see your best friend ro

Question

Constants PartA You're standing on an asteroid when you see your best friend rocketing by in her new spaceship. As she goes by, you notice that the front and rear of her ship coincide exactly with the 458 -m-diameter of another nearby asteroid that is stationary with respect to you. However, you happen to know that your friend's spaceship measured 500 m long in the showroom. What is your friend's speed relative to you? Express your answer using three significant figures. 999919 m/s Submit X Incorrect: Try Again; 5 attempts remaining

Explanation / Answer

The length contraction is given by

L = Lo*sqrt(1 - v^2/c^2)

Lo = proper length

L = contracted length

v = speed of friends space ship

L = Lo*sqrt(1 - v^2/c^2)

L/Lo = sqrt(1 - v^2/c^2)

458/500 = sqrt(1 - v^2/c^2)

sqrt(1 - v^2/c^2) = 0.916

taking square on both sides

(1 - v^2/c^2) = 0.916^2 = 0.839

v^2 / c^2 = 1 - 0.839

v^2 = 0.161c^2

v = sqrt(0.161)*c

v = 1.20 x 10^8 m/s

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