A rocket moves in the x-y plane, and has a velocity given by upsilon = (c/2, c/2

Question

A rocket moves in the x-y plane, and has a velocity given by upsilon = (c/2, c/2, 0). Consider a reference frame in which the velocity is c/2 to the right, in the positive x direction. (a) What are the components of the velocity of the rocket as perceived in the new reference frame? (b) From the perspective of the moving frame, what angle does the rocket make with respect to the x axis? (c) Answer the questions posed in parts (a) and (b), but from the point of view of a frame of reference moving to the left (i.e. in the negative x direction), with a velocity magnitude of c/2.

Explanation / Answer

a) velocity percieved in the reference frame = ( 0, c/2, 0)

b) angle which rocket makes with x-axis = cos theta = ( c/2 j ). i = 0, therefore theta

90 degree

c) if the reference frame is moving in -x drection, velocity = ( c, c/2 ,0), cos theta = ( c i + c/2 j ) . ( i), therefore

angle = 26.259 degree

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