Classical mechanics and conservation of momentum

[darkar]

Heres the question:

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 traveled by the boat, until the car falls off, is independent of the acceleration of the car.

My trying:
Since there's 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 don't get how to show that the distance moved is independence of the acceleration. Any help?

Thanks

 

[Doc Al]

My trying:
Since there's 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).

Write an expression for the total momentum of boat + car with respect to the water. Note that they want "a relation between the velocity of the car relative to the boat and the velocity of the boat relative to the water."

Then do the same thing to get the relationship between boat and water. But i don't get how to show that the distance moved is independence of the acceleration.

No matter what speed the car travels with respect to the boat, when the car gets to the end of the boat, the boat will have moved the same distance (with respect to the water). Hint: The center of mass of boat+car does not move.