(3-4)

①   Before the collision, both the rocks and Cormorant are flying parallel to the x-axis, so in Cormorant’s frame of reference, as in yours, the rocks have zero velocity in the y-direction and therefore no momentum in the y-direction. The total y-momentum is therefore zero before the collision.

②  After the collision:

(i)          Cormorant is still essentially keeping pace with rock A, so there is only a small velocity between them, and the time measurement he makes for rock A to move 1 metre from the x-axis is therefore not significantly affected by time dilation. So its y-velocity (= distance/time), from Cormorant’s perspective,  is just   v+­­yC(A) =  1/tC(A), and its y-momentum (= mass x velocity) is:

                                                                      p+yC(A)  =  mv+yC(A)  =  m/tC(A)  .

(ii)         Shag, who is keeping pace with rock B will measure a time equal to tC(A), for rock B to move 1 metre in the y-direction:       tS(B)  =  tC(A).  However Shag is moving rapidly relative to Cormorant, with a velocity u (which is overwhelmingly in the x-direction). Therefore the time (tC(B)) that passes for Cormorant while rock B moves 1 metre in the y-direction is dilated:

(iii)             Just as Nefertiti planned, there is no length contraction to bother us, because we are concerned with the y-direction, which is perpendicular to the direction of movement between the reference frames. So we can quite straightforwardly deduce rock B’s y-velocity in Cormorant’s reference frame (remember that the y-component of B’s velocity is in the opposite direction to A, so it is negative):

Hence, rock B’s y-momentum, in Cormorant’s frame of reference is:

③   Total y-momentum after collision is the sum of these two momenta:

which does not equal zero (which was the total before collision). Therefore- just as we knew would happen - momentum was apparently not conserved.