To determine the force exerted by the pump on the water, we can use the relationship between power, force, and velocity. The formula to calculate force is:
[tex]\[ \text{Force} = \frac{\text{Power}}{\text{Velocity}} \][/tex]
Given that:
- The power of the pump is [tex]\(3.4 \times 10^2\)[/tex] watts.
- The velocity at which water is lifted is [tex]\(7.5 \times 10^{-2}\)[/tex] meters/second.
Substituting these values into the formula, we get:
[tex]\[ \text{Force} = \frac{3.4 \times 10^2 \text{ watts}}{7.5 \times 10^{-2} \text{ m/s}} \][/tex]
When you compute this value, you find the force:
[tex]\[ \text{Force} = 4533.333333333334 \text{ newtons} \][/tex]
So the correct answer is option C.
[tex]\[ \boxed{4.5 \times 10^3} \text{ newtons} \][/tex]
