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Question

The velocity components of a particle moving in the xy plane of the reference frame K are equal to vx and vy. Find the velocity v of this particle in the frame K which moves with the velocity V relative to the frame K in the positive direction of its x axis.

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Solution

By the velocity addition formula:
vx=vxV1Vvxc2, vy=vy1V2c21vxVc2
And, v=vx2+vy2=(vxV)2+v2y(1V2c2)1vxVc2

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