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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 massM = 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.

Assuming the car accelerates with a constant acceleration a = 4 m/s^2 relative to the boat.

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.

My trying:

Since theres no external force, the Momentum of the center of Mass frame stay the same at initial and final state. Then i got the velocity of the car as -(20/3) x V(boat at final).

Then do the same thing to get the relationship between boat and water. But i dont get how to show that the distance moved is independence of the acceleration. Any help?

Thanks