In a strange cycling event (called a “Madison”) one cyclist intentionally has a

Question

In a strange cycling event (called a “Madison”) one cyclist intentionally has a perfectly elastic collision with his team-mate (this as a ‘tag-team’ sort of event). Two cyclists, Tom & Frank have paired up to compete in a Madison. Tom’s mass is 73.9 kg, and Frank’s is 59.3 kg. During one of the ‘collisions’ Tom is racing at 40 mph (17.9 m/s) east, when he ‘collides’ with Frank who cruising along at 13 mph (5.81 m/s) in the same direction as Tom. What is the final velocity of each cyclist?

In this problem, one cyclist holds his arm out, the other grabs it and flings himself forward...just to clear up what a madison is.

I am having trouble with this whole problem, I know there is something about exchanging force or momentum, but I'm not sure.

Explanation / Answer

Masses m = 73.9 kg             M = 59.3 kg Initial velocites u = 17.9 m/ s                       U = 5.81 m/ s Let the velocities of the after collision be v and V For elastic collision coefficient of restitution e = 1                                         ( V - v) / ( u - U ) = 1                                                          V - v = u - U                                                                     = 12.09                                                                  V = v + 12.09        --------( 1) From law of conservation of momentum , mu + MU = mv + MV                                                 1322.81 + 344.533 = 73.9 v +59.3 ( v +12.09)                                                              1667.343 = 133.2 v + 716.937                                                                              v = 7.135 m / s From eq( 1) , V = 19.225 m/ s

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