Answer :
To determine how much horsepower is required to achieve 864.36 joules of work, let's go through the solution step by step.
1. Understand the relationship between joules, watts, and horsepower:
- 1 watt (W) is equivalent to 1 joule per second (J/s).
- 1 horsepower (hp) is approximately 745.7 watts (W).
2. Calculate the power in watts required for the task:
- Given that work done is 864.36 joules and it is being done in 1 second, this means:
[tex]\[ \text{Power (in watts)} = \frac{\text{Work (in joules)}}{\text{Time (in seconds)}} = \frac{864.36 \, \text{J}}{1 \, \text{s}} = 864.36 \, \text{W} \][/tex]
3. Convert the power from watts to horsepower:
- Using the conversion factor, 1 horsepower = 745.7 watts:
[tex]\[ \text{Power (in horsepower)} = \frac{\text{Power (in watts)}}{\text{Conversion factor}} = \frac{864.36 \, \text{W}}{745.7 \, \text{W/hp}} \approx 1.159 \, \text{hp} \][/tex]
4. Compare the calculated power with the given answer choices:
- The closest value to 1.159 hp in the given options is:
- A. [tex]$864.36 \, \text{hp}$[/tex]
- B. [tex]$441 \, \text{hp}$[/tex]
- C. [tex]$0.59 \, \text{hp}$[/tex]
- D. [tex]$1.16 \, \text{hp}$[/tex]
Given our calculation, the closest answer is D. [tex]$1.16 \, \text{hp}$[/tex].
Thus, the best answer is:
[tex]\[ \boxed{1.16 \, \text{hp}} \][/tex]
1. Understand the relationship between joules, watts, and horsepower:
- 1 watt (W) is equivalent to 1 joule per second (J/s).
- 1 horsepower (hp) is approximately 745.7 watts (W).
2. Calculate the power in watts required for the task:
- Given that work done is 864.36 joules and it is being done in 1 second, this means:
[tex]\[ \text{Power (in watts)} = \frac{\text{Work (in joules)}}{\text{Time (in seconds)}} = \frac{864.36 \, \text{J}}{1 \, \text{s}} = 864.36 \, \text{W} \][/tex]
3. Convert the power from watts to horsepower:
- Using the conversion factor, 1 horsepower = 745.7 watts:
[tex]\[ \text{Power (in horsepower)} = \frac{\text{Power (in watts)}}{\text{Conversion factor}} = \frac{864.36 \, \text{W}}{745.7 \, \text{W/hp}} \approx 1.159 \, \text{hp} \][/tex]
4. Compare the calculated power with the given answer choices:
- The closest value to 1.159 hp in the given options is:
- A. [tex]$864.36 \, \text{hp}$[/tex]
- B. [tex]$441 \, \text{hp}$[/tex]
- C. [tex]$0.59 \, \text{hp}$[/tex]
- D. [tex]$1.16 \, \text{hp}$[/tex]
Given our calculation, the closest answer is D. [tex]$1.16 \, \text{hp}$[/tex].
Thus, the best answer is:
[tex]\[ \boxed{1.16 \, \text{hp}} \][/tex]
