$(10)$ Jabba the Hutt decides he needs to get better fuel mileage on his sand barge. He has an air deflector installed on top of the barge to accomplish this. This increases the fuel mileage of a barge from $4$ miles$/$gal to $4\mathrm{.}25m\frac{i}{g}al$ at $55$ mph $.$ The engine provides $11,000,000ft*lb$ of energy to drive the barge from every gallon of fuel. One$-$half of this energy is used to overcome the drag resistance of the air on the barge. Find the drag coefficient for the barge with and without the air deflector. The barge has a frontal area of $82f{t}^2.$