Final answer:
A motor that produces 15.0 hp will take approximately 6.95 seconds to lift a 1275 lb object 45.0 feet.
Step-by-step explanation:
To calculate how much time is required to lift a 1275 lb (pound) object 45.0 ft with a motor that produces 15.0 hp (horsepower), we need to consider the work done by the motor and the power it provides. The weight of the object in pounds can be converted to a force in Newtons; however, as this is a US customary unit problem, we can work directly with horsepower and feet. Since 1 horsepower is equivalent to 550 foot-pounds per second, we can use this to find the time required.
First, we convert the weight from pounds to foot-pounds of work. The work done in lifting the object is weight (in pounds) multiplied by height (in feet), which is 1275 lb × 45.0 ft = 57375 foot-pounds.
Next, we convert the power of the motor from horsepower to foot-pounds per second: 15.0 hp × 550 foot-pounds/sec = 8250 foot-pounds per second.
To find the time required to do the work, we divide the total work by the power of the motor:
Time = Total work / Power = 57375 foot-pounds / 8250 foot-pounds/sec = 6.95 seconds
Therefore, the motor will take approximately 6.95 seconds to lift a 1275 lb object a distance of 45.0 feet.