a) Rosita, on the surface of the Earth, sees Elmo fly away from Earth in his spa

Question

a) Rosita, on the surface of the Earth, sees Elmo fly away from Earth in his spaceship at 0.9c. According to the clock on Elmo's spaceship, he giggles once every 10s. As Rosita sees it, how much time elapses between Elmo's giggles?

b) Elmo sees Zoe's spaceship flying away from Earth at 0.8c relative to him. What speed does Rosita measure for Zoe's spaceship?

c) According to Elmo's meterstick, his spaceship is 50 m long. According to Zoe, how long is Elmo's spaceship?

d) Elmo then sees The Count flying toward Earth at 0.9c. According to the count's pocket watch, he counts an item on his spaceship once every second. According to Rosita, how much time elapses between each of these events?

Explanation / Answer

(a)
Using time dilation,
t = to/sqrt(1 - v^2/c^2)
t = 10/sqrt(1 - 0.9^2)
t = 22.95 s

(b)
Speed measure by Rosita, = (u + v)/(1 + u*v/c^2)
= (0.9 + 0.8) / (1 + 0.8*0.9)
= 0.988 c

(c)
L = Lo * sqrt(1 - v^2/c^2)
L = 50 * sqrt(1 - 0.9^2)
L = 21.8 m

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