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*) write out the solution on paper step by step;
*) clearly show all steps using variable notation and algebraic manipulation whenever possible;
*) express the solution in symbolic form; and
*) substitute numerical values in the last step (not the first) so as to obtain the numerical results.

In the following problem, assume the mass of the package is MT, the mass of the cart is M2, the vertical fall distance is H, the angle of the ramp is 8, the initial speed of the package is V 10 and the initial speed of the cart is V Express the answers in terms 20 of these quantities (and gO. Assume the cart includes a mass-less pillow which provides a cushion between the cart and the package. 8.87 CP In a shipping company distribution center, an open cart of mass 50.0 kg is rolling to the left at a speed of 5.00 m/s Fig. P8.87). Ignore friction between the cart and the floor. A 15.0-kg package slides down a chute that is inclined at 37 from the horizontal and leaves the end of the chute with a speed of 3.00 m/s. The package lands in the cart and they roll together. If the lower end of the chute is a vertical distance of 4.00 m above the bottom of the cart, what are (a) the speed of the package just before it lands in the cart and (b) the final speed of the cart? Figure P8.87 4.00 m

Answer the following additional questions assuming the system is comprised of the cart and the package:


a) is the x-component of the momentum of the package conserved before the collision? Explain (briefly).
b) is the x-component of the momentum of the cart conserved before the collision? Explain.
c) is the y-component of the momentum of the package conserved before the collision? Explain.

d) is the y-component of the momentum of the cart conserved before the collision? Explain.
e) is the x-component of the momentum of the system conserved during the collision? Explain.
f) is the y-component of the momentum of the system conserved during the collision? Explain.

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