The figure shows a side view of a galaxy that is 50 lightyears (50 LY) in diamet

Question

The figure shows a side view of a galaxy that is 50 lightyears (50 LY) in diameter. This value for the diameter is itsproper length. A spaceship enters the galactic plane with speed0.995c relative to the galaxy. Assume that the galaxy can betreated as an intertial reference frame. Note: A light year is thedisntace that light travels through vacuum inone year; that is, 1light year = c x (1 year).

How long does it take the spaceship to cross the galaxyaccording to a clock on board the spaceship?
a. 5.02 years b. 12.5 years c. 49.8 years d. 50.3 years e. 90.0 years

will give points to anyone who answers but the lifesaver tothe person who gives most information.

Explanation / Answer

proper length L = 50 LY speed v = 0.995 c relative length L ' = L [ 1 - ( v / c ) ^ 2]                           = 4.9937 LY required time t = L ' / v                       = 4.9937 * c * Y / ( 0.995 c )                       = 5.0188 Y                      = 5.02 Years

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