When cars are equipped with flexible bumpers, they will bounce off each other du

Question

When cars are equipped with flexible bumpers, they will bounce off each other during low-speed collisions, thus causing less damage. In one such accident, a 1750kg car traveling to the right at 1.50m/s collides with a 1350kg car going to the left at 1.10m/s . Measurements show that the heavier car's speed just after the collision was 0.250m/s in its original direction. You can ignore any road friction during the collision.

What was the speed of the lighter car just after the collision?

Calculate the change in the combined kinetic energy of the two-car system during this collision.

Explanation / Answer

Let's write the momentum conservation equation:
m1v1 + m2v2 = m1V1 + m2V2
with
m1 = 1750 kg
m2 = 1350 kg
v1 = 1.50 m/s
v2 = - 1.10 m/s
V1 = 0.250 m/s

Then
V2 = (m1v1 + m2v2 - m1V1) / m2 =
= (1750*1.50 - 1350*1.10 - 1750*0.250) / 1350 = 0.52m/s (to the right)

Kinetic energy before the collision:
K1 = 1/2 m1v1

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