Physics
posted by John .
A fireman, 45.1 m away from a burning building, directs a stream jet of water from a ground level fire hose at an angle of 34.1 degrees above the horizontal.
The acceleration of gravity is 9.8 m/s^2.
If the speed of the stream as it leaves the hose is 58.8 m/s, at what height will the stream of water strike the building?
Answer is: 26.3309 m
Not sure how to get the answer; how do I know when the water is headed back down? Is there a way to integrate velocity and find where the slope is equal to zero? If so, is velocity a function of time or distance here? If someone could give me the general equation and show me how to apply it that would be great.

First figure out how long it take the water to reach the wall of the building.
That time T is 45.1 m/(58.8 cos34.1 m/s) T = 0.926269 s
Use the equation for vertical height vs time to determine where it is when it hits the building.
Y = Vo*sin34.1*T  (1/2)gT^2
= 58.8*0.56064*0.926269 s
 (1/2)(9.80)(0.926269)
= 30.535  4.543 = 26.0 m
There are too many significant figures in your answer. You did not mention the elevation of the hose where the water left it. That would have to be added to the result.