A hot air balloon rising straight up from a level field is tracked by a range finder located a horizontal distance of 500m from the lift-off point. At the moment the range-finder's elevation angle is pi/4 , the angle is increasing at a rate of 0.14 rad/min. How fast is the balloon rising at the moment?

A75-hp (shaft output) motor that has an efficiency of 91.0 percent is worn out and is to be replaced by a high-efficiency motor that has an efficiency of 95.4 percent. the motor operates 4368 hours a year at a load factor of 0.75. taking the cost of electricity to be $0.12/kwh, determine the amount of energy and money saved as a result of installing the high-efficiency motor instead of the standard motor. also, determine the simple payback period if the pu