Heidi T. answered • 03/21/20

MS in Mathematics, PhD in Physics, 7+ years teaching experience

Conservation of moment says that the total momentum of the system (both vehicles) before the collision is equal to the total momentum of the system (both vehicles) after the collision. Before the collision, the two vehicles have different velocities, so are treated separately. The car has momentum p_{ci} = m_{c} v_{ci} and the truck has momentum p_{ti}= m_{t} v_{ti} =0

The total momentum of the system before the collision is the sum of the momentums of the two:

p_{i} = p_{ci} + p_{ti} = m_{c} v_{ci} + m_{t} v_{ti} = (1500 kg)(10 m/s) + (2250 kg)(0) = 15,000 kg m/s

After the collision the two vehicles are stuck together so move off together. Their individual masses have not changed and can be combined in the final situation and the velocity of both is the same value:

p_{f} = (m_{c} + m_{t}) v_{f}

Conservation of momentum says that p_{i} = p_{f} = 15,000 kg m/s

so we can write: (m_{c} + m_{t}) v_{f } = 15,000 kg m/s then solve for v_{f }

v_{f } = (15,000 kg m/s) / (m_{c} + m_{t}) = (15,000 kg m/s) / (1500 kg + 2250 kg) = 4.0 m/s