A truck of mass 1.3 104 kg, travelling at 9.0 101 km/h [N], collides with a car of
mass 1.1 103 kg, travelling at 3.0 101 km/h [N]. If the collision is completely
inelastic, what are the magnitude and direction of the velocity of the vehicles immedi-
ately after the collision?
To solve this problem, we need to use the principle of conservation of momentum. In an inelastic collision, the total momentum before the collision is equal to the total momentum after the collision.
The initial momentum of the truck is given by:
P_initial = m_truck * v_truck
P_initial = (1.3 * 10^4 kg) * (9.0 * 10^1 km/h) = 1.17 * 10^6 kg*km/h
The initial momentum of the car is given by:
P_initial = m_car * v_car
P_initial = (1.1 * 10^3 kg) * (3.0 * 10^1 km/h) = 3.3 * 10^4 kg*km/h
The total initial momentum is the sum of the momenta of the truck and car:
P_initial_total = 1.17 * 10^6 kg*km/h + 3.3 * 10^4 kg*km/h = 1.203 * 10^6 kg*km/h
Since the collision is completely inelastic, the truck and car stick together after the collision. Let their common final velocity be V_final.
The final momentum is then given by:
P_final_total = (m_truck + m_car) * V_final
P_final_total = ((1.3 * 10^4 kg) + (1.1 * 10^3 kg)) * V_final
P_final_total = 1.41 * 10^4 kg * V_final
According to the conservation of momentum principle:
P_initial_total = P_final_total
1.203 * 10^6 kg*km/h = 1.41 * 10^4 kg * V_final
V_final = (1.203 * 10^6 kg*km/h) / (1.41 * 10^4 kg) = 85.32 km/h
Therefore, the magnitude of the velocity of the vehicles immediately after the collision is 85.32 km/h. Since they stuck together, the direction of the velocity is the same as the initial direction of the momentum, which is to the right [N].