Question

The script for an action movie calls for a small race car (of mass 1500 kg and length 3.0 m) to accelerate along a flat-top boat (of mass 4200 kg and length 24 m), 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 advisor for the movie. The boat will initially touch the dock, as in the figure below. The boat can slide through the water without significant resistance and both the car and the boat can be 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.

Answer 1

there is no external force acting on the system, so the postion of center of mass will remain same,

let assume that the edge of dock is chosen as the origin, Xcmi= initial position of center of mass

Mc= 1500 kg, Mb= 4200, total mass of system= Mt= 1500 +4200=5700Kg

center of mass of car is at its center, so its distance from dock= 24- 3/2= 24-1.5

distance of Center of mass of boat from dock= 24/2= 12 m

so Xcmi= [Mc (24-1.5) + Mb(24/2)]/Mt

Xcmi=[1500(24-1.5) + 4200 (24/2)]/5700

Xcmi= 14.8 m

now lets assume the boat moves a distance L from the dock,

Xcmf= [Mc (x+1.5) + Mb(12+x)]/Mt

now Xcmi= Xcmf=14.8m

14.8 =[1500 (x+1.5) + 4200(12+ x)]/5700

14.8(5700)= 1500x+ 2250 + 50400 + 4200x

84360= 5700x + 52650

84360-52650= 5700 x

31710 = 5700x

x= 31710/5700

x= 5.56 m