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Answer :
Sure! Let's break this down into a step-by-step solution for the question:
1. Identify the Given Values:
- The machine has a maximum power output of 1005 foot-pounds per second.
- The object is being pushed with a force of 115 pounds.
- The distance the object is pushed is 12 feet.
2. Calculate the Work Done:
- Work is calculated using the formula:
[tex]\[
\text{Work} = \text{Force} \times \text{Distance}
\][/tex]
- Plug in the values:
[tex]\[
\text{Work} = 115 \, \text{lbs} \times 12 \, \text{ft} = 1380 \, \text{ft-lbs}
\][/tex]
3. Determine the Time Required:
- We use the formula for power, which relates power, work, and time:
[tex]\[
\text{Power} = \frac{\text{Work}}{\text{Time}}
\][/tex]
- Rearrange the formula to solve for time:
[tex]\[
\text{Time} = \frac{\text{Work}}{\text{Power}}
\][/tex]
- Plug in the values:
[tex]\[
\text{Time} = \frac{1380 \, \text{ft-lbs}}{1005 \, \text{ft-lbs/sec}} \approx 1.37 \, \text{seconds}
\][/tex]
4. Select the Closest Option:
- The calculated time, approximately 1.37 seconds, is closest to 1.4 seconds in the multiple-choice options given.
Therefore, it will take approximately 1.4 seconds for the machine to push the object the given distance.
1. Identify the Given Values:
- The machine has a maximum power output of 1005 foot-pounds per second.
- The object is being pushed with a force of 115 pounds.
- The distance the object is pushed is 12 feet.
2. Calculate the Work Done:
- Work is calculated using the formula:
[tex]\[
\text{Work} = \text{Force} \times \text{Distance}
\][/tex]
- Plug in the values:
[tex]\[
\text{Work} = 115 \, \text{lbs} \times 12 \, \text{ft} = 1380 \, \text{ft-lbs}
\][/tex]
3. Determine the Time Required:
- We use the formula for power, which relates power, work, and time:
[tex]\[
\text{Power} = \frac{\text{Work}}{\text{Time}}
\][/tex]
- Rearrange the formula to solve for time:
[tex]\[
\text{Time} = \frac{\text{Work}}{\text{Power}}
\][/tex]
- Plug in the values:
[tex]\[
\text{Time} = \frac{1380 \, \text{ft-lbs}}{1005 \, \text{ft-lbs/sec}} \approx 1.37 \, \text{seconds}
\][/tex]
4. Select the Closest Option:
- The calculated time, approximately 1.37 seconds, is closest to 1.4 seconds in the multiple-choice options given.
Therefore, it will take approximately 1.4 seconds for the machine to push the object the given distance.
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