1. A spaceship moving at 90% of the speed of light (or 0 . 9 c ) passes by a spa

Question

1. A spaceship moving at 90% of the speed of light (or 0.9c) passes by a space station. The ship is 450 m long in its rest frame.

(a) How long does the spaceship appear to be as viewed from the space station?

(b) The space station sends out a series of light blinks, at a frequency of one blink per second. What apparent speed of these blinks do the crew on the moving spaceship observe?

(c) The space ship launches a probe traveling at 0.8c) relative to the ship, in the same direction that the ship is traveling in. What speed is observed for the probe by the space station?

Explanation / Answer

Part A)
Apply L = L'(sqrt( 1 - v^2/c^2)

L = (450)(sqrt (1 - .9^2)

L = 196.2 m

Part B

Apply t = t'/sqrt(1 - v^2/c^2)

1 = t'/(sqrt 1 - .9^2)
t = .436 sec per blink (frequency = 2.30 Hz)

Part C)
Apply u = v + u'/(1 + vu'/c^2)

u = (.9c + .8c)/(1 + .9(.8))

u = .988 c

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