Question

question 10
2 pts
if it took 2 minutes to hoist an aircraft weighing 1500 lbs to a vertical height of 7 feet, how much power was used?
428.57
.08
5250

Explanation:

Step1: Recall Power Formula

Power \( P \) in foot - pounds per minute is given by the formula \( P=\frac{Work}{Time} \), and work \( W \) done against gravity is \( W = F\times d \), where \( F \) is the force (weight of the object) and \( d \) is the distance. So \( P=\frac{W\times h}{t} \), where \( W = 1500\) lbs (weight), \( h = 7\) feet (height), and \( t = 2\) minutes (time).

Step2: Calculate Work

First, calculate the work done. \( W_{work}=1500\times7 = 10500\) foot - pounds.

Step3: Calculate Power

Now, use the power formula. \( P=\frac{10500}{2}= 5250\)? Wait, no, wait. Wait, maybe we are using horsepower or another unit? Wait, no, wait, maybe I made a mistake. Wait, the formula for power in foot - pounds per second: 1 horsepower = 550 foot - pounds per second. But the time is in minutes. Let's convert minutes to seconds. 2 minutes = 120 seconds. Work is \( 1500\times7 = 10500\) foot - pounds. Then power in foot - pounds per second is \( \frac{10500}{120}\approx87.5\), but that's not one of the options. Wait, maybe the formula is using foot - pounds per minute. Then \( P=\frac{1500\times7}{2}=\frac{10500}{2} = 5250\) foot - pounds per minute. But the options have 428.57, 0.08, 5250. Wait, maybe the question is using horsepower? Wait, 1 horsepower = 550 foot - pounds per second. Let's recalculate. Work is 10500 foot - pounds. Time is 2 minutes = 120 seconds. Power in horsepower is \( \frac{10500}{120\times550}=\frac{10500}{66000}\approx0.159\), no. Wait, maybe the formula is \( P=\frac{W\times h}{t\times550}\) for horsepower? Wait, no, let's check the options. Wait, the first option is 428.57, second 0.08, third 5250. Wait, maybe I messed up the formula. Wait, let's re - examine. The weight is 1500 lbs, height 7 feet, time 2 minutes. The formula for power (in some context) could be \( P=\frac{1500\times7}{2\times1.0}\)? No, wait, maybe the question is using the formula for power as \( P=\frac{W\times h}{t}\) where \( W \) is weight, \( h \) is height, \( t \) is time in minutes, but then 1500*7=10500, 10500/2 = 5250. But that seems high. Wait, no, maybe the question is using a different approach. Wait, maybe the formula is \( P=\frac{W\times h}{t\times 12}\)? No, that doesn't make sense. Wait, let's check the options again. The options are 428.57, 0.08, 5250. Wait, maybe the question is using the formula for power in kilowatts? No, that's not. Wait, maybe I made a mistake in the formula. Wait, let's calculate \( \frac{1500\times7}{2\times1.0}=5250\), which is one of the options (the third option). So maybe the formula is \( P = \frac{Weight\times Height}{Time}\) with time in minutes, so \( P=\frac{1500\times7}{2}=5250\) foot - pounds per minute.

Answer:

5250 (the third option, assuming the formula \( P=\frac{Weight\times Height}{Time} \) with time in minutes)