Question

A car and a lorry are about to collide. When they collide the two vehicles become tightly locked together. The lorry is going at a speed of 20km/h and weighs 9.5 tonnes. The car is going at a speed of 40km/h and is 0.5 tonnes. Calculate the speed of the vehicles immediately after the collision. (6 marks)

Answer 1

Answer:

The speed of the vehicles immediately after the collision is 5.84 m/s.

Explanation:

The speed of the vehicles after the collision can be found by conservation of linear momentum:

$p_{i} = p_{f}$

$m_{1}v_{1_{i}} + m_{2}v_{2_{i}} = m_{1}v_{1_{f}} + m_{2}v_{2_{f}}$

Where:

m₁: is the mass of the car = 0.5 ton = 500 kg

m₂: is the mass of the lorry = 9.5 ton = 9500 kg

$v_{1_{i}}$: is the initial speed of the car = 40 km/h = 11.11 m/s

$v_{2_{i}}$: is the initial speed of the lorry = 20 km/h = 5.56 m/s

$v_{1_{f}}$: is the final speed of the car =?

$v_{2_{f}}$: is the final speed of the lorry =?    

Since the two vehicles become tightly locked together after the collision $v_{1_{f}}$ = $v_{2_{f}}$:

$m_{1}v_{1_{i}} + m_{2}v_{2_{i}} = v(m_{1} + m_{2})$

$v = \frac{m_{1}v_{1_{i}} + m_{2}v_{2_{i}}}{m_{1} + m_{2}} = \frac{500 kg*11.11 m/s + 9500 kg*5.56 m/s}{500 kg + 9500 kg} = 5.84 m/s$

Therefore, the speed of the vehicles immediately after the collision is 5.84 m/s.

I hope it helps you!