A car of mass m = 1200 kg and length l = 4 m is positioned such that its rear end is at the end of a flat-top boat of mass M = 8000 kg and length L = 18 m. Both the car and the boat are initially at rest and can be approximated as uniform in their mass distributions and the boat can slide through the water without significant resistance.

(a) Assuming the car accelerates with a constant acceleration a = 4 m/s2 relative to the boat, how long does it take before the centre of mass of the car reaches the other end of the boat (and therefore falls off)?

(b) What distance has the boat travelled relative to the water during this time?

(c) Use momentum conservation to find a relation between the velocity of the car relative to the boat and the velocity of the boat relative to the water. Hence show that the distance travelled by the boat, until the car falls off, is independent of the acceleration of the car.