Question

Light requires 4.5 years to travel from the nearest star to earth. If we could travel there in a spaceship going 90% of the speed of light, the trip would require 5.0 years according to clocks on earth. How much time would pass for the passengers in the ship

Answer 1

Time according to earth clock (T0) = 0.22 years (Approx)

Step-by-step explanation:

Given:

Time taken by light = 4.5 years

Time taken by ship = 5 years

Speed of light = c

Speed of ship (v) = 90% of c = 0.9c

Find:

Time according to earth clock (T0) = ?

Computation:

Time dilation is ,

`T(Difference) = \frac{T0}{\sqrt{1-(v^2)/(c^2) } }\\\\ (5-4.5)= \frac{T0}{\sqrt{1-((0.9c)^2)/(c^2) } }\\\\ 0.5=(T0)/(√(1-0.81) )\\\\T0 =0.2179`

Time according to earth clock (T0) = 0.22 years (Approx)