A spaceship makes the long trip from earth to the nearest star system, Alpha Cen

Question

A spaceship makes the long trip from earth to the nearest star system, Alpha Centauri, at a speed of 0.925 c. The star is about 4.37 light-years from earth, as measured in earth’s frame of reference (1 light-year is the distance light travels in a year). Part A How many years does the trip take according to an observer on earth? Express your answer, with the appropriate units, to three significant figures. t = 4.72 yr SubmitMy AnswersGive Up Correct Part B How many years does the trip take according to a passenger on the spacecraft. How many light-years distant is Alpha Centauri from earth, as measured by a passenger on the speeding spacecraft? Hint 1. Note that, in the ship’s frame of reference, the passengers are at rest, while the space between earth and Alpha Centauri goes rushing past at 0.925 c. NB ( Enter your answer using dimensions of distance.)

Explanation / Answer

A) distance = 4.37 light years

v = 0.925c

time = (4.37 light years) / (0.925 c) = 4.72 years

B) as observer is moving with high speed. so there will be time dilation.

t = t0 / Y

Y = 1/ sqrt[1 - (v/c)^2] = 1 / sqrt[1 - 0.925^2] = 2.63

t = 4.72 / 2.63 = 1.79 years

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