To determine the power of the motor, we use the basic power formula:
[tex]\[ \text{Power} = \text{Force} \times \text{Velocity} \][/tex]
We are given the following values:
- Force ([tex]\( F \)[/tex]) = [tex]\( 5.75 \times 10^3 \)[/tex] newtons
- Velocity ([tex]\( v \)[/tex]) = 22 meters/second
Substituting the given values into the power formula:
[tex]\[ \text{Power} = (5.75 \times 10^3 \, \text{N}) \times (22 \, \text{m/s}) \][/tex]
Let's carry out the multiplication:
[tex]\[ \text{Power} = 5.75 \times 22 \times 10^3 \][/tex]
[tex]\[ \text{Power} = 126.5 \times 10^3 \][/tex]
[tex]\[ \text{Power} = 126500 \, \text{watts} \][/tex]
Next, we compare this result, 126500 watts, to the given answer choices and determine which one is the closest:
A. [tex]\( 7.9 \times 10^4 \)[/tex] watts = 79000 watts
B. [tex]\( 1.3 \times 10^5 \)[/tex] watts = 130000 watts
C. [tex]\( 2.5 \times 10^5 \)[/tex] watts = 250000 watts
D. [tex]\( 3.7 \times 10^5 \)[/tex] watts = 370000 watts
E. [tex]\( 5.0 \times 10^5 \)[/tex] watts = 500000 watts
The correct answer is the one that is closest to 126500 watts.
Among the given options, [tex]\( 1.3 \times 10^5 \)[/tex] watts or 130000 watts (answer B) is the closest to 126500 watts.
Therefore, the correct answer is:
B. [tex]\( 1.3 \times 10^5 \)[/tex] watts
