The figure shows a side view of a galaxy that is 50.0 light years in diameter. T

Question

The figure shows a side view of a galaxy that is 50.0 light years in diameter. This value for the diameter is its proper length. A spaceship enters the galactic plane with speed 0.995c relative to the galaxy. Assume that the galaxy can be treated as an inertial reference frame. Note: A light year is the distance that light travels through vacuum in one year; that is, 1 light year = c

The figure shows a side view of a galaxy that is 50.0 light years in diameter. This value for the diameter is its proper length. A spaceship enters the galactic plane with speed 0.995c relative to the galaxy. Assume that the galaxy can be treated as an inertial reference frame. Note: A light year is the distance that light travels through vacuum in one year; that is, 1 light year = c times (1 year). How long does it take the spaceship to cross the galaxy according to an observer at rest in the galaxy? Please Explain

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 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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