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A powered winch is used to pull a sailboat to shore. The winch uses a [tex][tex]$900 \, W$[/tex][/tex] motor.

If the motor is used for [tex][tex]$30 \, s$[/tex][/tex], how much work does it do? (Power: [tex]P = \frac{W}{t}[/tex])

A. [tex]0.03 \, J[/tex]
B. [tex]30 \, J[/tex]
C. [tex]960 \, J[/tex]
D. [tex]27,000 \, J[/tex]

Sagot :

GinnyAnswer
To solve this question, we need to understand the relationship between power, work done, and time. The formula connecting these quantities is:

[tex]\[ \text{Power} (P) = \frac{\text{Work done} (W)}{\text{Time} (t)} \][/tex]

Given:
- Power ([tex]\(P\)[/tex]) = 900 W
- Time ([tex]\(t\)[/tex]) = 30 s

We are asked to find the work done ([tex]\(W\)[/tex]). Rearanging the formula to solve for work done, we have:

[tex]\[ W = P \times t \][/tex]

Now we can substitute the given values into the equation:

[tex]\[ W = 900 \, \text{W} \times 30 \, \text{s} \][/tex]

[tex]\[ W = 27000 \, \text{Joules} \][/tex]

Therefore, the work done by the motor is [tex]\(27,000 \, \text{J}\)[/tex].

The correct answer is:

[tex]\[ 27,000 \, \text{J} \][/tex]
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