Question

The closest known star to our solar system is Alpha Centauri, which is approximately 4.30 light years away. Spaceship A, with a constant speed of 0.800c relative to the Earth and a proper length of 100 m, travels from Earth to this star. Spaceship B with a constant speed of 0.600c relative to the Earth travels from Earth to this star.
(a) How much time would elapse during Spaceship A’s trip on a clock on Earth?

(b) How much time would elapse during Spaceship A’s trip on a clock on Spaceship B?

(c) How long is Spaceship A for an observer at rest on Spaceship B

Answer 1

for part a) Find out the time taken ,then using time dilation formula,time taken by spaceship A when clock is on earth.

Part b) we have to find time taken by spaceship when clock is on spaceship B ,for this we have to find velocity of Spaceship A when measured on B which is calculated using inverse L-T.

After that putting that velocity in time dilation formula,time taken is calculated.

Part c) using length contraction ,length of Spaceship A when measured from B is calculated.Here, velocity v is velocity of Spaceship A w.rt B which is already calculated in part b.