A dump truck is sitting at the top of a hill, and its parking brake disengages. It rolls down a hilland collides with an empty, stationary car. The car sticks to the grill of the truck and the two continue movingforward. The dump truck has mass (mt = 4000kg) and is travelling at 5mswhen it hits the car. The car hasmass (mc = 1500kg).
(a) Why does the truck roll down the hill? Answer this very carefully using energy arguments.
(b) What is the speed of the truck/car immediately after the collision?
(c) What is the momentum of the truck/car in the frame of reference of a jogger approaching the collisionat 2ms(opposite the truck's initial velocity)?
(d) How fast, and in which direction, would the jogger have to run for the momentum of the system toappear to him to be zero?
(e) What is the momentum of the car and truck system prior to the collision in the center of mass frame?
(f) Relative to an observer standing on the street, how much of the initial kinetic energy of the system isconvertible? Does this answer depend on the frame of reference of the observer, why or why not?
(g) Relative to an observer standing on the street, how much of the initial kinetic energy of the system must be conserved to conserve momentum? Does this answer depend on the frame of reference of theobserver, why or why not?