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: v′x=vx−V1−Vvxc2, v′y=vy√1−V2c21−vxVc2 And, v′=√v′x2+v′y2=√(vx−V)2+v2y(1−V2c2)1−vxVc2