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At an amusement park there are 200-kg bumper cars A, B, and C that have riders with masses of 55 kg, 90 kg, and 42.5 kg respectively. Car A is moving to the right with a velocity vA = 2 m/s and car C has a velocity vC = 1.5 m/s to the left, but car B is initially at rest. The coefficient of restitution between each car is 0.8. Determine the final velocity of each car, after all impacts, assuming car A hits car B before car C does. Assume positive sign denoting forward motion and negative sign denoting backward motion.

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Answer:

Vb = 0.334 m/s

Va = -1.265 m/s

Vc = 1.424 m/s

Explanation:

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Initial momentum = 255(2) – 242.5(1.5) = 146.25

Final momentum = 255Va + 290Vb + 242.5 Vc = 146.25

Vb - Va = 0.8(2) = 1.6

Vc - Vb = 0.8(1.5) = 1.2

Va = Vb -1.6

Vc = Vb + 1.2

255(Vb -1.6) + 290Vb + 242.5(Vb + 1.2) = 146.25

255 Vb – 408 + 290 Vb + 242.5 Vb + 291 = 146.25

787.5 Vb = 263.25

Vb = 0.334 m/s

Va = Vb -1.6 = 0.334 – 1.6 = -1.265 m/s

Vc = Vb + 1.2 = 0.224 + 1.2 = 1.424 m/s

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