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182. Problem 2.33 (R) One cosmic-ray particle approaches the Earth along its axis with a velocity of 0.8 c toward the North Pole and another with a velocity 0.6 c toward the South Pole. We have to find the relative speed of approach of one particle with respect to the other. |
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Solution: Click For PDF Version Let us consider an inertial frame of reference which is at rest with respect
to the cosmic-ray particle which to an observer on Earth is approaching it along
its axis toward the North Pole. Let us call this frame of reference S. with
respect to this frame of reference the inertial frame of reference in which the
Earth is stationary,
We have to calculate the speed of the other cosmic-ray particle,
According to the velocity addition theorem
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, will be
moving toward it with velocity
. In
.
,
as measured by an observer in S. This speed will be the relative speed
between the two cosmic-ray particles.