Given two observers O and O?, with O? moving at uniform velocity ? in the positive x-direction relative to O, use the appropriate Lorenz transformations to show that if an object is moving with velocity component in the frame of reference of O?, then

where u, is the corresponding velocity component according to O.

(a) A space ship is launched from Earth and maintains a uniform velocity of 0.900c. The space ship subsequently launches a small rocket in the forward direction with a speed of 0.900c relative to the ship. What is the speed of the small rocket relative to the Earth?

(b) According to observations on the Earth, the nearest star to the solar system is 4.25 light years away. A space ship which leaves the Earth and travels at uniform velocity takes 4.25 years, according to ship-borne clocks, to reach the star. What is the speed of the space ship, expressed as a fraction of the speed of light c?

Transcribed Image Text:

U, + v 1.