Question

A spaceship at rest on the earth has a length of 120m and a mass of 16,000kg. Then the spaceship begins to move away from the earth at 3/4 speed of light.

If the spaceship sends out a second ship away from the earth on what observers on the spaceship think is 1/2 speed of light, how fast do the observers on earth think the second ship is moving?

If the spaceship sends out a second ship toward the earth at what observers on the spaceship think is 9/10 the speed of light, how fast do the observers on earth think the second ship is moving?

Answer 1

Given :-

           Velocity of the spaceship is  

          and let the velocity of the second spaceship observed by an observer on the earth is

          As both the spaceships are moving with relativistic speed, we must determine the speed of second spaceship by using relativistic velocity addition instead of simple non-relativistic addition. We have relativistic velocity addition formula given as,

                          where,    velocity of second spaceship observed by observer in the spaceship.

                                           is the speed of light

• If the spaceship sends out a second ship away from the earth :-

As the spaceship and second spaceship are moving away from the earth i.e in the same direction, so we can have

Therefore, the observers on earth think the second ship is moving with velocity of    or .

• If the spaceship sends out a second ship toward from the earth :-

As the spaceship is moving away from the earth and second spaceship is moving toward the earth i.e in the different direction, so we can have

Therefore, the observers on earth think the second ship is moving with velocity of    or .