A fire hose is turned on the door of a burning building in order to knock the door down. This requires a force of 1000. N. If the hose delivers 40. liters per second, what is the maximum velocity of the stream needed, assuming the water doesn't bounce back?
A) 50. m/s
B) 25 m/s
C) 15. m/s
D) 40. m/s
E) 30. m/s

Question

Quizplus · Accepted Answer

The force exerted by the water 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 change in time. Since the water doesn't bounce back, the change in momentum is given by $\Delta p = m \cdot v$, where $m$ is the mass of the water and $v$ is its velocity. The mass flow rate of the water is $40 \, \text{liters per second} = 40 \, \text{kg/s}$ (since 1 liter of water has a mass of approximately 1 kg). Thus, $F = m \cdot v / \Delta t = 40 \cdot v$. Setting this equal to 1000 N (the force needed to knock down the door) and solving for $v$ gives $v = 1000 / 40 = 25 \, \text{m/s}$.

A Fire Hose Is Turned on the Door of a Burning