Question

A car of mass 1000kg is traveling in a northward (+y) direction with a constant speed of 10m/s. It then hits a stationary truck. The truck is twice as heavy as the car. After the collision, the car travels in a direction 30 degrees East of North and the truck travels 60 degrees West of North.

a) What are the final speeds of the car and the truck after collision?

b) Calculate the change in kinetic energy of the system before and after collision.

c) Based on your answer in part (b), what type of collision do you think this is?

Answer 1

(a) Given the mass of the car m1 = 1000kg, the initial velocity of the car u1 = 10m/s, the mass of the truck = 2 x m1 = 2000kg, the initial velocity of the truck u2 = 0 (rest). Let v1 and v2 be the final velocities of the car anf truck respectively after collision. The diagram of collision is shown below.

From the figure, applying conservation of momentum along x-direction,

Appying conservation of momentum along y-direction,

So the final speed of the truck is 2.50m/s.

So the final speed of the car is 8.65m/s.

(b) The Kinetic energy of the system before collision is

The Kinetic energy of the system before collision is

(c) It is clear that the kinetic energy after collision is greater than the kinetic energy before collision. So it is an inelastic collision in two dimension.