Answer:
.
Explanation:
Because the track is level and frictionless, the net force on this car-load system will be zero in the horizontal direction. As a result, (by Newton's Second Law of mechanics,) the total momentum of this system in the horizontal direction will stay the same.
Momentum of the car-load system in the horizontal direction, before contact:
- Car: .
- Load: zero (for it is dropped "vertically.")
Combine the two parts to obtain: .
Because the load stays on the car, the car and the load should have the same horizontal velocity after contact. Let denote that velocity. Momentum of the system after contact:
- Car: .
- Load: .
Combine to obtain:
.
Because the total momentum of the system will stay the same:
.
Solve for to obtain:
.
In other words, the new velocity of the system would be .