Calvin and Hobbes set up wagons on two different hills, as shown in the figure. Hobbes's wagon, with mass M, starts at a height 2H on the hill that makes an angle 2θ with the horizontal. Calvin's wagon, with mass 2M, starts at a height H on the hill that makes an angle θ with the horizontal. At Calvin's signal, both he and Hobbes push their wagons from rest and let them roll down the hill. (Since they will collide, Calvin and Hobbes do not ride in the wagons, but watch them safely from the tops of the hills.) The wagons roll towards each other, collide in the middle, where the ground is horizontal, and stick together. As you answer the following questions, you may neglect any friction forces or air resistance. (a) After the wagons collide, do they move to the left, to the right, or remain at rest? Justify your answer.

For parts (b) and (c), consider the time interval between when the wagons began moving and when they collided.

(b) For the system consisting of Calvin's wagon, Hobbes's wagon, and Earth, does the total mechanical energy increase, decrease, or remain the same? Justify your answer.

(c) For the system consisting only of Calvin's wagon and Hobbes's wagon, does the total mechanical energy increase, decrease, or remain the same? Justify your answer.