Question

A 1000 kg car running at 50 km/h eastward has head-on collision with a 2000 kg truck running at 30 km/h. If the two vehicles are locked together after collision, calculate the final velocity of the wreckage. What is the loss in kinetic energy of the system?

Answer 1

The final velocity can be found by momentum conservation. The positive direction of motion os counted according to the direction of motion of the car.

$$mv-Mu=(M+m)s,\\\space\\ s=\frac{mv-Mu}{M+m}=-3.3\text{ km/h (or 3.3 km/h West)}$$

The loss in the energy:

$$\Delta E=\frac12 mv^2+\frac12Mu^2-\frac12(M+m)s^2=165\text{ kJ}.$$