An automobile of mass 1500 kg moving at 25 m/s collides with a truck of mass 450

Question

An automobile of mass 1500 kg moving at 25 m/s collides with a truck of mass 4500 kg at rest. The bumpers of the two vehicles lock together during the crash. Compare the force exerted by the car on the truck with that exerted by the truck on the car during the collision. Is on force larger than the other or are they equal in magnitude to each other? What is the final velocity of the car and truck just after the collision. Now this time the car and the truck bounce off each other completely elastically. Compare the force exerted by the car on the truck with that exerted by the truck on the car during the collision. Is one force larger than the other or are they equal in magnitude? What are the final velocities of the car and truck just after the collision?

Explanation / Answer

1)both the forces are same.

2)1500*25 = (1500+4500)v

v = 25/4 = 6.25 m/s

3)coefficient of restitution e = (v2-v1)/(u1-u2).For an elastic collision e=1
v2-v1 = u1-u2 = 25-0 = 5
v2-v1=25---->(1)
m1u1 + m2u2 = m1v1+m2v2
1500*25 +0 = 1500*v1 + 4500v2
v1 + 3v2 =25--->(2)
solving (1) and (2)
v1 = -12.5 m/s
v2 = 12.5 m/s

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