The script for an action movie calls for a small car race (of mass 1500kg and le

Question

The script for an action movie calls for a small car race (of mass 1500kg and length 3.0m) to accelerate along a flattop boat (of mass 4000 kg and length 14m), from one end to the other, where the car will then jump the gap between the boat and a somewhat lower dock. You are the technical supervisor for the movie. The boat will initially touch the dock. The boat can slide through the water without significant resistance; both the car and the boat can approximated as uniform in their mass distribution. Determine what the width of the gap will be just as the car is about to make the jump. 

Explanation / Answer

In order for the car to move forward it needs to apply anequal force backwards. Let's say the car accelerates at a rate of 20m/s^2. then theforce applied to the boat will be 20m/s^2 x 1500kg=30000N The car moves 14M so the time required for it to clearthe boat is x=1/2at^2 t=2x/a =2(14M)/20m/s^2=1.18s so 3x10^4N will be applied for 1.18s. That force will bemoving a total of 5500kg, giving the boat an acceleration ofa=F/m=5.45m/s^2 x=1/2at^2=1/2(5.45m/s^2)(1.18s)^2=3.794m So given that acc for the car, the boat will be 3.794m fromthe dock I tried it with an acc of 40m/s^2 and I got 3.818m So I'm going with 3.8m

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