Mr Davis 97
- 1,461
- 44
Homework Statement
A fire truck pumps a stream of water on a burning building at a rate K kg/s. The stream leaves the truck at an angle ##\theta## with respect to the horizontal and strikes the building horizontally at height h above the nozzle. What is the magnitude of the force on the truck due to the ejection of the water stream?
Homework Equations
The Attempt at a Solution
We know that the rate of change of momentum of the water coming out of the nozzle must be equal and opposite to the force on the truck, from Newton's third law, then ##\vec{F_{truck}} = -\dot{\vec{P}}##. Now, we know that ##\dot{\vec{P}} = K \vec{v_0}##, so now all we must do is find the magnitude of the initial velocity. In the y-direction, we know that the velocity of the stream is zero when y = h (since it hits the building horizontally. So we can use the equation ##v_y^2 = v_{0y}^2 - 2gh##. Since the final velocity at h is zero, we can solve for the initial velocity in the y-direction, which is just ##v_{0y} = \sqrt{2gh}##. And since ##v_{0y} = v_0 \sin \theta##, we have that ##v_0 = \frac{\sqrt{2gh}}{\sin \theta}##. Thus, the magnitude of ##\dot{P}## and thus of ##F_{truck}## is ##K \frac{\sqrt{2gh}}{\sin \theta}##
I feel like I am doing something wrong...