A car of mass 1000kg is travelling in an eastward ( x) direction with a constant speed of 20m/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 300 North of East and the truck travels 600 South of East. (a) What are the final speeds of the car and the truck after collision

4.33 m/s, 5 m/s

Explanation:

mass of car, m = 1000 kg

initial velocity of car, u = 20 m/s along east

mass of truck, M = 2 x mass of car = 2000 kg

initial velocity of truck, U = 0 m/s

After collision, the velocity of car is v and the direction is 30° North of east.

The velocity of truck is V and the direction is 60° South of east.

Use conservation of momentum along X axis.

m x u = m x v x Cos 30 + M x V x Cos 60

1000 x 20 = 1000 x v x 0.866 + 2000 x V x 0.5

20 = 0.866 v + V   (1)

Use conservation of momentum along y axis

0 = m x v x Sin 30 - M x V x Sin 60

0 = 1000 x v x 0.5 - 2000 x V x 0.866

v = 3.464 V     (2)

Substitute the value of v in equation (1)

20 = 0.866 x 3.464 V + V

V = 5 m/s

v = 0.866 x 5 = 4.33 m/s

Thus, the final speed of car is 4.33 m/s and the final speed of truck is 5 m/s after the collision.