Answer :
To determine the power output of the lawnmower engine, we can use the formula for power, which is:
[tex]\[ P = \frac{W}{t} \][/tex]
where:
- [tex]\( P \)[/tex] is the power output,
- [tex]\( W \)[/tex] is the work done, and
- [tex]\( t \)[/tex] is the time taken.
Given values:
- Work done ([tex]\( W \)[/tex]) = 4,560,000 Joules
- Time ([tex]\( t \)[/tex]) = 20 minutes
First, we need to convert the time from minutes to seconds because the standard unit of power (Watt) is Joules per second.
[tex]\[ t = 20 \text{ minutes} \times 60 \text{ seconds per minute} = 1200 \text{ seconds} \][/tex]
Next, we use the formula [tex]\( P = \frac{W}{t} \)[/tex] to calculate the power output.
[tex]\[ P = \frac{4560000 \text{ Joules}}{1200 \text{ seconds}} \][/tex]
[tex]\[ P = 3800 \text{ Watts} \][/tex]
So, the power output of the engine is 3800 Watts.
Now, let's compare our calculated power output to the given options:
1. 3800 W
2. 228,000 W
3. 91,200,000 W
4. 547,200,000 W
The power output we calculated (3800 Watts) matches the first option. Therefore, the correct power output of the lawnmower engine is:
[tex]\[ \boxed{3800 \text{ Watts}} \][/tex]
[tex]\[ P = \frac{W}{t} \][/tex]
where:
- [tex]\( P \)[/tex] is the power output,
- [tex]\( W \)[/tex] is the work done, and
- [tex]\( t \)[/tex] is the time taken.
Given values:
- Work done ([tex]\( W \)[/tex]) = 4,560,000 Joules
- Time ([tex]\( t \)[/tex]) = 20 minutes
First, we need to convert the time from minutes to seconds because the standard unit of power (Watt) is Joules per second.
[tex]\[ t = 20 \text{ minutes} \times 60 \text{ seconds per minute} = 1200 \text{ seconds} \][/tex]
Next, we use the formula [tex]\( P = \frac{W}{t} \)[/tex] to calculate the power output.
[tex]\[ P = \frac{4560000 \text{ Joules}}{1200 \text{ seconds}} \][/tex]
[tex]\[ P = 3800 \text{ Watts} \][/tex]
So, the power output of the engine is 3800 Watts.
Now, let's compare our calculated power output to the given options:
1. 3800 W
2. 228,000 W
3. 91,200,000 W
4. 547,200,000 W
The power output we calculated (3800 Watts) matches the first option. Therefore, the correct power output of the lawnmower engine is:
[tex]\[ \boxed{3800 \text{ Watts}} \][/tex]
