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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:
[tex] p_{i} = p_{f} [/tex]
[tex] m_{1}v_{1_{i}} + m_{2}v_{2_{i}} = m_{1}v_{1_{f}} + m_{2}v_{2_{f}} [/tex]
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
[tex]v_{1_{i}}[/tex]: is the initial speed of the car = 40 km/h = 11.11 m/s
[tex]v_{2_{i}}[/tex]: is the initial speed of the lorry = 20 km/h = 5.56 m/s
[tex]v_{1_{f}}[/tex]: is the final speed of the car =?
[tex]v_{2_{f}}[/tex]: is the final speed of the lorry =?
Since the two vehicles become tightly locked together after the collision [tex]v_{1_{f}}[/tex] = [tex]v_{2_{f}}[/tex]:
[tex] m_{1}v_{1_{i}} + m_{2}v_{2_{i}} = v(m_{1} + m_{2}) [/tex]
[tex] 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 [/tex]
Therefore, the speed of the vehicles immediately after the collision is 5.84 m/s.
I hope it helps you!