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description: show all you work, including units, on separate paper. follow the \problem solving meth this final exam is cumulative and covers material from the entire course.
instructions: from the list of choices, select the one best answer.
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question 36
what is the power rating of a 150 lb person who walks up a 15 ft tall staircase in 10 sec?
○ 0.23 hp
○ 0.72 hp
○ 0.13 hp
○ 0.41 hp

Explanation:

Step1: Calculate Work Done

Work \( W \) is force times distance. Here, force is weight (\( F = 150\ \text{lb} \)) and distance \( d = 15\ \text{ft} \). So \( W = F \times d = 150\ \text{lb} \times 15\ \text{ft} = 2250\ \text{ft-lb} \).

Step2: Calculate Power in ft-lb/s

Power \( P \) is work over time. Time \( t = 10\ \text{sec} \), so \( P = \frac{W}{t} = \frac{2250\ \text{ft-lb}}{10\ \text{sec}} = 225\ \text{ft-lb/s} \).

Step3: Convert to Horsepower (hp)

We know that \( 1\ \text{hp} = 550\ \text{ft-lb/s} \). So \( P_{\text{hp}} = \frac{225\ \text{ft-lb/s}}{550\ \text{ft-lb/s per hp}} \approx 0.41\ \text{hp} \)? Wait, no, wait: Wait, 225 divided by 550: \( \frac{225}{550} \approx 0.409 \approx 0.41 \)? Wait, no, wait, maybe I miscalculated. Wait, 15015=2250, 2250/10=225. Then 225/550 ≈ 0.409, but wait the options have 0.41? Wait no, wait maybe I made a mistake. Wait, no, let's check again. Wait, 150 lb 15 ft = 2250 ft-lb. Time is 10 s. So power is 2250/10 = 225 ft-lb/s. Then, 1 hp = 550 ft-lb/s. So 225 / 550 = 0.409, which is approximately 0.41 hp? Wait but wait, the options: 0.23, 0.72, 0.13, 0.41. Wait, maybe I messed up. Wait, no, wait 150*15=2250, 2250/10=225. 225/550=0.409≈0.41. So the power is approximately 0.41 hp.
Wait, but wait, let me recalculate: 15015=2250. 2250/10=225. 225 divided by 550: 5500.4=220, 550*0.41=225.5. Oh, so 225 is close to 225.5, so 0.41 hp. So the correct answer should be 0.41 hp.

Answer:

0.41 hp (the option with 0.41 hp, e.g., if the options are labeled as: the last option, say D. 0.41 hp, then the answer is D. 0.41 hp)