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168.

Problem 21.23 (RHK)

A spaceship, at rest in a certain reference frame S, is given a speed increment of 0.500 c. It is then given a further 0.500 c increment in this new frame. This process is continued until its speed with respect to the original frame S exceeds 0.999 c. We have to find the number of increments that are required.

Solution:             Click For PDF Version

We will solve this problem by using relativistic velocity addition successively. When the spaceship has been given the first speed increment of 0.500 c the speed of its rest frame with respect to S will be 0.500 c. In the spaceship is given a speed increment of 0.500 c. Let the rest frame of the spaceship be now. Using velocity addition we calculate the speed of with respect to S. It will be

In the frame the spaceship is given a speed increment of 0.500 c. Let the new rest frame of the spaceship be called . The speed of with respect to S will be

In the frame the spaceship is given a speed increment of 0.500 c. Let the new rest frame of the spaceship be called . The speed of with respect to S will be

In the frame the spaceship is given a speed increment of 0.500 c. Let the new rest frame of the spaceship be called . The speed of with respect to S will be

In the frame the spaceship is given a speed increment of 0.500 c. Let the new rest frame of the spaceship be called . The speed of with respect to S will be

In the frame the spaceship is given a speed increment of 0.500 c. Let the new rest frame of the spaceship be called . The speed of with respect to S will be

Thus we find that seven increments of 0.5 c are required to enable a spaceship at rest to attain speed of 0.999 c.