(3-4) Here, our two frames of reference are going to be based on Cormorant (frame C) and on Shag (frame S). The symbols can get a bit messy here, so let’s agree that, for example, vyC(A) means the y-component of the velocity of rock A, in Cormorant’s frame of reference. Shag is flying in the opposite direction to Cormorant, at high velocity, so his frame of reference is moving relative to Cormorant’s frame: let’s say that the relative velocity of the two seabirds – and hence of their frames of reference - is u. The two rocks, A and B each has a mass of m.
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In the picture above, the blue lines show the trajectories of the two rocks in Cormorant's frame of reference.
① Deduce the y-component of the momentum of each rock, and hence the total y-momentum , from Cormorant’s point of view, before the collision.
② Following the collision, each of the seabirds is going to measure the y-velocity of the rock he’s keeping pace with by using a stopwatch to time how long it takes for the rock to move 1 metre (perpendicular distance) away from the x-axis. Let’s say that Cormorant measures a time tC(A) for rock A to achieve this. By symmetry, therefore, Shag measures the same time for rock B: so tC(A) = tS(B). Now find expressions for:
(i) The y-velocity, v+yC(A), of rock A in Cormorant’s frame of reference, following the collision, and hence its y-momentum, p+yC(A).
(ii) The time taken, tC(B), for rock B to travel its 1 metre, in Cormorant’s frame of reference, taking account of the relativistic effect of the high relative velocity of this frame, relative to Shag’s.
(iii) The y-velocity, v+yC(B), of rock B, in Cormorant’s frame of reference, and hence its y-momentum, p+yC(B).
③ Hence deduce the total y-momentum of the two rocks after the collision. Is momentum conserved, in Cormorant’s frame of reference?
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