A 1200 kg car travels at 25.0 m/s and collides head-on in a perfectly inelastic collision with a stationary 2400 kg truck. The kinetic energy lost in the collision is
A) 330,000 J.
B) 250,000 J.
C) 125,000 J.
D) 95,000 J.
E) 75,000 J.

Question

Quizplus · Accepted Answer

In a perfectly inelastic collision, the two objects stick together and move with a common velocity after the collision. Using conservation of momentum, we can find the common velocity to be 8.33 m/s. The initial kinetic energy of the car is (1/2)(1200 kg)(25.0 m/s)^2 = 468,750 J. The initial kinetic energy of the truck is 0. Therefore, the total initial kinetic energy is 468,750 J. After the collision, the combined mass is 3600 kg and moving with a velocity of 8.33 m/s. The final kinetic energy can be found to be (1/2)(3600 kg)(8.33 m/s)^2 = 113,390 J. Therefore, the kinetic energy lost in the collision is 468,750 J - 113,390 J = 355,360 J, which is closest to choice B (250,000 J).

A 1200 Kg Car Travels at 25