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
