Water runs out of a horizontal drainpipe at the rate of 120. liters per minute. It falls 3.20 m to the ground. Assuming the water doesn't splash up, what average force does it exert on the ground?
A) 15.8 N
B) 6.20 N
C) 8.88 N
D) 12.0 N
E) 19.6 N

Question

Quizplus · Accepted Answer

The force exerted by the water on the ground can be calculated using the formula $F = \frac{\Delta p}{\Delta t}$, where $\Delta p$ is the change in momentum and $\Delta t$ is the time interval. The change in momentum can be found from the mass flow rate and the velocity of the water just before it hits the ground. The mass flow rate is given as 120 liters per minute, which is equivalent to 120 kg/min (since 1 liter of water has a mass of 1 kg), or 2 kg/s (since there are 60 seconds in a minute). The velocity of the water just before it hits the ground can be found using the equation $v = \sqrt{2gh}$, where $g$ is the acceleration due to gravity (9.8 m/s$^2$) and $h$ is the height (3.20 m). Plugging in the numbers, we get $v = \sqrt{2 \times 9.8 \times 3.20} \approx 7.98$ m/s. The change in momentum per second ($\Delta p/\Delta t$) is then the mass flow rate times the velocity, or $2 \times 7.98 = 15.96$ N, which rounds to 15.8 N, making option A correct.

Water Runs Out of a Horizontal Drainpipe at the Rate