Two observers, A on earth and B in a spacecraft whose speed is 2.00 x 108 m/s, both set their watches to the same time when the ship is abreast of the earth.

(a) How much time must elapse by A's reckoning before the watches differ by 1.00 s?

(b) To A, B's watch seems to run slow. To B, does A's watch seem to run fast, run slow, or keep the same time as his own watch?

Remember that the non-relativistic approximation is not valid here, u/c = 2/3.

(a) With t representing both the time measured through A and the time as measured in A's frame for the clock in B's frame to advance by t_o, we require

by it t = 3.93 s.

(b) A moving clock appears always to run slower. In such problem, the time t is the time which observer A measures the time as B's clock takes to record a time vary of t_o.