Select the best answer for the question.

864.36 J of work are needed to accomplish a task. Approximately how much horsepower is required to achieve this task?

A. 1.16 hp
B. 441 hp
C. 864.36 hp
D. 0.59 hp



Answer :

To determine the approximate amount of horsepower required to accomplish a task where 864.36 joules of work is needed, we need to convert the energy value in joules to horsepower. Here's the step-by-step process:

1. Understand the Conversion Factor:
The conversion factor between joules per second (watts) and horsepower is essential. 1 horsepower (hp) is equivalent to 745.7 watts (joules per second).

2. Convert Joules to Horsepower:
We need to convert the given energy in joules to horsepower. To do this, we'll divide the energy in joules by the number of joules per horsepower.

[tex]\[ \text{Horsepower} = \frac{\text{Work in joules}}{\text{Conversion factor}} \][/tex]

Given:
[tex]\[ \text{Work} = 864.36 \, \text{J} \][/tex]
and
[tex]\[ 1 \, \text{hp} = 745.7 \, \text{W} \][/tex]

The formula to find the horsepower is:

[tex]\[ \text{Horsepower} = \frac{864.36}{745.7} \][/tex]

3. Calculation:
Performing the division:

[tex]\[ \text{Horsepower} \approx 1.159 \][/tex]

4. Determine the Closest Answer:
Now, compare the calculated value with the provided options:
- A. 1.16 hp
- B. 441 hp
- C. 864.36 hp
- D. 0.59 hp

We can see that 1.159 hp is very close to 1.16 hp given in Option A.

Therefore, the best answer is:
A. 1.16 hp