I'm working on a physics problem in preparation for the MCAT and there's this particular problem that's troubling me. I don't know if it's a bad question or if I'm not understanding some sort of concept. I was hoping someone here can clarify. Here's the problem verbatim:
A 1kg cart travels down an inclined plane at 5 m/s and strikes two billiard balls, which start moving in opposite directions perpendicular to the initial direction of the cart. Ball A has a mass of 2kg and moves away at 2m/s and ball B has a mass of 1kg and moves away at 4m/s. Which of the following statements is true?
a) the cart will come to a halt in order to conserve momentum
b) the cart will slow down
c) the cart will continue moving as before, while balls A and B will convert the gravitational potential energy of the cart into their own kinetic energies
d) these conditions are impossible because they violate either the law of conservation of momentum or conservation of energy
At first glance, it appears to me that the answer is (D) because the system seemingly has more total momentum after the collision than before the collision. However, the answer explanation insists the correct answer to be (C) since it claims that "kinetic energy is not conserved; the system gains energy in this inelastic collision".
I can understand that this gain in energy can come from gravitational potential energy from the incline the cart is on; however, it is ambiguous if the cart is accelerating down the incline. In order for the scenario to be consistent with choice (C), does the cart have to be accelerating down the incline? Or do you take the problem to mean that the cart is leaving the incline at 5m/s? Or am I missing or not understanding something?
How would you interpret this problem and which explanation do you think is most consistent with the scenario? What assumptions do you have to make to arrive at your answer?
The answer key's explanation, verbatim is as follows:
The law of conservation of momentum states that both the vertical and horizontal components of momentum for a system must stay constant. If you take the initial movement of the cart as horizontal and the two balls move in perpendicular directions to the horizontal, it means that the cart must maintain its horizontal component of velocity. Therefore, (A) and (B) are wrong. If the billiard balls move as described, then kinetic energy is not conserved; the system gains energy in this inelastic collision. (C) correctly describes how this scenario is possible.