A small experimental vehicle has a total weight W of 1225 lb including wheels and driver. Each of the four wheels has a weight of 85 lb and a centroidal radius of gyration of 20 in. Total frictional resistance R to motion is 94 lb and is measured by towing the vehicle at a constant speed on a level road with engine disengaged. Determine the power output of the engine for a speed of 35 mi/hr up the 13-percent grade (a) with zero acceleration and (b) with an acceleration of 8 ft/sec2. (Hint: Power equals the time rate of increase of the total energy of the vehicle plus the rate at which frictional work is overcome.)

An external consultant recommends that a plant installs a bank of capacitors for power factor correction. this will reduce the peak electrical demand charges by an average of 93 kw every month. the plant current pays $13 per kw in peak demand charges. the capacitor bank will include 223 kw of fixed capacitors, and 183 of variable capacitors. the fixed capacitors cost $59 per kw, and the variable capacitors will cost $65 per kw. the consultant charges 21% of the equipment costs to install the capacitors. because this project will reduce the demand for the electric utility, they are prepared to provide a one-time rebate of $42 per kw of reduced demand. what is the simple payback period for this project (in years)?