Final answer:
Using the formula for power, the elevator moved a total distance of 32.2 meters.
Step-by-step explanation:
To calculate how far the elevator moved using the given power and time, we should apply the formula for power in terms of work done over time. The power provided by the elevator is defined as the rate at which it does work, which is the product of the force and the distance moved (height) divided by time:
Power = Work/Time
Where Work = Force × Distance.
Since the elevator is only lifting itself and the passengers vertically, the force in question is the weight of the elevator acting downwards due to gravity.
First, calculate the total force acting on the elevator, which is the weight of the passenger plus the weight of the elevator:
Total weight = Weight of passenger + Weight of elevator
Total weight = 750 N + 22,000 N = 22,750 N
Next, rearrange the power equation to solve for distance:
Distance = (Power × Time) / Force
Insert the known values into the equation:
Distance = (7,700 W × 95 s) / 22,750 N
Distance = 732,500 J / 22,750 N
Distance = 32.2 meters
Therefore, the elevator moved a total distance of 32.2 meters.