Two bumper cars are gliding (unpowered) on a frictionless track. The left bumper

Question

Two bumper cars are gliding (unpowered) on a frictionless track. The left bumper car has slid,from rest,down the hill to gain a speed of 7.8 m/s, while the right bumper car is stationary. The left car (including occupant) has a mass of 72 kg while the right one has a mass of 93 kgand the pedestrian has a mass of 64 kg. After the bumper cars collide, the right car moves to the right where it hits the unsuspecting pedestrian, who falls and lands on top of the right bumper car.

1.1) [10] How high was the hill?

1.2) [10] How fast is the right bumper car going after the left bumper car hits it?

1.3) [10] How fast is the right bumper car going after it runs into the pedestrian?

Explanation / Answer

1.1) At the top of the hill bumper car has only potential energy which is converted into kinetic energy when it reaches to the bottom of the hill. so,

PE = KE

mgh = mv2/2

h = v2/(2g) = 7.82/(2*9.8) = 3.104 m

1.2) Momentum before the collision = 72*7.8 = 561.6 kg.m/s

Momentum after the collision = 93 * v

From conservation of momentum we have,

93v = 561.6

v = 6.039 m/s

1.3)

Momentum before the collision = 93*6.039 = 561.6 kg.m/s

Momentum after the collision = (93+64) * v

From conservation of momentum we have,

157v = 561.6

v = 3.577 m/s

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