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Chapter 37: Q85P (page 1151)

One cosmic-ray particle approaches Earth along Earth’s north-south axis with a speed of 0.80ctoward the geographic north pole, and another approaches with a speed of 0.60c toward the geographic south pole (Fig. 37- 34). What is the relative speed of approach of one particle with respect to the other?

Short Answer

Expert verified

The speed of one particle relative to another is0.95c.

Step by step solution

01

Relativistic velocity addition:

Suppose an object is moving with the velocity u' with respect to S' frame, which is moving with the velocity v with respect to frame S then the velocity of the object u with respect to S frame is,

role="math" localid="1663136206277" u=u'+v1+u'vc2

02

Determine the relative velocity:

Let’s consider the rest frame of 0.6cparticle moving towards the south-pole to be Sframe. And the earth frame is called S'frame.

In S frame, earth is moving towards it with velocity v=0.6c and relative to this S' frame a particle is moving towards the North pole with speed u'=0.8c.

Then the velocity of this same particle relative to Sframe is,

u=0.8c+0.6c1+0.80.6=1.4c1.48=0.946c

Hence, the speed of one particle relative to other is 0.95c.

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Most popular questions from this chapter

The length of a spaceship is measured to be exactly half its rest length. (a) To three significant figures, what is the speed parameter βof the spaceship relative to the observer’s frame? (b) By what factor do the spaceship’s clocks run slow relative to clocks in the observer’s frame?

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