The distance to a particular star, as measured in the earth\'s frame of referenc

Question

The distance to a particular star, as measured in the earth's frame of reference, is 7.11 light years (1 light year is the distance light travels in 1 year).  A spaceship leaves earth headed for the star, and takes 3.35 years to arrive, as measured by passengers on the ship.

(a) How long does the trip take, according to observers on earth?

Answer: 8.34 years

(b) What distance for the trip do passengers on the spacecraft measure (Hint: What is the speed of light in units of ly/y)

Answer: 3.02 ly (light years)

How do you find these numbers?!

Explanation / Answer

distance =7.11 years .

let the ship move with velocity v

now length is contracted .so length which the starship people they travel = L(1-v^2/c^2)

now length = time *velocity

so L(1-v^2/c^2)=3.35*v

calculating this we get v=.9014c

now given time which star chip people think they trvel is 3.35 years now time which earth people think is

3.35/(1-v^2/c^2) which will turn out to come as 8.34 Lyr

b)Length which starship people think they travel is 7.11(1-v^2/c^2) ..hopw this cleared your doubt ... and please don't mind my english i am in a hurry

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