Reproduce Example 4.1 in Mi and Masrur: Consider a planetary gear train based transmission with an engine (carrier) providing 100kW at 2000rpm optimum operating point. The ring gear has 72 teeth and the sun gear has 30 teeth. The final drive ratio is 3.7865, and the wheel radius is 0.283m. (1) For a vehicle speed of 45mph or 20.6m/s, the power demand under heavy acceleration at this speed is 120kW. Find the speed and power for each component, assuming no losses. (2) For a vehicle speed of 70mph, or 32.7m/s, when cruising, the power demand is 70kW. Calculate the speed and power of each component.