A pump is required to lift 600text{ kg} of water per minute from a well 25text{ m} deep and eject it with a speed of 50text{ m/s}. The power of the p…

Mass per second $\frac{dm}{dt} = \frac{600\text{ kg}}{60\text{ s}} = 10\text{ kg/s}$. Total energy per second (Power) = Potential energy per second + Kinetic energy per second = $\frac{dm}{dt}gh + \frac{1}{2} \frac{dm}{dt}v^2$. $P = (10)(10)(25) + \frac{1}{2}(10)(50)^2 = 2500 + 12500 = 15000\text{ W} = 15\text{ kW}$? Wait: $\frac{1}{2}(10)(2500) = 12500$, total $= 15000\text{ W} = 15\text{ kW}$. Let's check options: A is 15 kW. Let's re-verify: $2500 + 12500 = 15000\text{ W} = 15\text{ kW}$. Correct answer is A.