To solve this problem, we start with the formula for power, which is given by:
[tex]\[ P = \frac{W}{t} \][/tex]
Where:
- [tex]\( P \)[/tex] is the power,
- [tex]\( W \)[/tex] is the work done,
- [tex]\( t \)[/tex] is the time.
Rearranging the formula to solve for work done, we get:
[tex]\[ W = P \times t \][/tex]
Next, substitute the given values into this equation. We know:
- The power [tex]\( P \)[/tex] is 900 Watts (W),
- The time [tex]\( t \)[/tex] is 30 seconds (s).
So, we plug these values into the formula:
[tex]\[ W = 900 \, \text{W} \times 30 \, \text{s} \][/tex]
Now, calculate the product:
[tex]\[ W = 27000 \, \text{J} \][/tex]
Thus, the work done by the winch is:
[tex]\[ 27000 \, \text{J} \][/tex]
Therefore, the correct answer is:
[tex]\[
27,000 \, \text{J}
\][/tex]
