Firefighter's Water Stream Strike Height Calculation

AI Thread Summary
To calculate the height at which a firefighter's water stream strikes a building, the horizontal and vertical components of the water's velocity must be analyzed. The horizontal distance to the building is 44.0 m, and the water is directed at an angle of 31.2° with an initial speed of 40.0 m/s. The horizontal velocity is calculated as v(x) = v * cos(31.2°), while the vertical velocity is v(y) = v * sin(31.2°). The range formula R = (v * sin²(31.2°)) / g can be used to determine the height of the stream upon impact. The height does not require the building's height, only the calculated height of the water stream at the given distance.
jitto92
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Homework Statement


A firefighter, 44.0 m away from a burning building, directs a stream of water from a ground level fire hose at an angle of 31.2° above the horizontal. If the speed of the stream as it leaves the hose is 40.0 m/s, at what height will the stream of water strike the building?
v=40.0m/s
v(x)=vcos31.2
v(y)=vsin31.2
g=9.81

Homework Equations


R=(vsin^2(31.2))/g
x(t)=vcos(31.2)


The Attempt at a Solution


I have tried breaking it down to x and y components but it doesn't make sense if the height of the building and its distance from the firefighter is not given !
 
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jitto92 said:
I have tried breaking it down to x and y components but it doesn't make sense if the height of the building and its distance from the firefighter is not given !
(1) The distance from the firefighter is given.
(2) You don't need the height of the building, just the height of the stream as it hits the building.
 

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