Question

An engine pumps water continuously through a hose. If the speed with which the water passes through the hose nozzle is \( v \), and if \( k \) is the mass per unit length of the water jet as it leaves the nozzle, what is the rate at which kinetic energy is being imparted to the water?

• A. \( 2kv^2 \)
• B. \( 2kv^3 \)
• C. \( 2kv^4 \)
• D. None

Hint:

To find the rate of energy imparted to a moving fluid, use the formula for kinetic energy and multiply by the velocity of the fluid.

Answer 1

The Correct Option is A

The kinetic energy imparted to the water per unit time is given by: \[ P = \frac{1}{2} k v^2 \cdot v = \frac{1}{2} k v^3 \] Thus, the rate at which kinetic energy is being imparted to the water is \( 2kv^3 \).