Physics Velocity Question

Question

A 1,500 kg car travelling at a velocity of 10m/s hits into a 2,250 kg truck that is at rest. Assume the bumpers lock together so that the collision is completely inelastic and that momentum is conserved. What is the velocity of the two cars after the collision?*

Answer 1

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