A pair of bumper cars in an amusement park ride collide elastically as one appro

Question

A pair of bumper cars in an amusement park ride collide elastically as one approaches the other directly from the rear, as seen in part (a) of the figure below

One has a mass of m1 = 437 kg and the other m2 = 536 kg, owing to differences in passenger mass. If the lighter one approaches at v1 = 4.53 m/s and the other is moving atv2 = 3.75 m/s,

A/ Calculate the velocity of the lighter car after the collision.

B/ Calculate the velocity of the heavier car after the collision.

C/ Calculate the change in momentum of the lighter car.

D/ Calculate the change in momentum of the heavier car.

Explanation / Answer

v1' = (v1(m1-m2) + 2m2v2)/(m1+m2)

v2'= (v2(m2-m1) + 2m1v1)/(m1+m2)

a) v1' = 3.67 m/s

b) v2' = 4.45 m/s

c)change in momentum = m1(v1'-v1) = -375.82 kgm/s

d) change in momentum = m2(v2'-v2) =375.2 kgm/s

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