A brush fire is burning on a rock ledge on one side of a ravine that is 40 m wid

Question

A brush fire is burning on a rock ledge on one side of a ravine that is 40 m wide. A fire truck sits on the opposite side of the ravine at an elevation 8.5 m above the burning brush. The fire hose nozzle is aimed 35 above horizontal, and the firefighters control the water velocity by adjusting the water pressure. Because the water supply at a wilderness fire is limited, the firefighters want to use as little as possible.

At what speed should the stream of water leave the hose so that the water hits the fire on the first shot?

Explanation / Answer

Let the speed = v m/s
Horizontal Component of velocity = v*cos(35) m/s
Vertical Component of velocity = v*sin(35) m/s

Horizonal distance to cover = 40 m
Vertical distance to cover = 8.5 m

Time taken to cover , Vertical distance = t
t = 40 /  v*cos(35) -

This time is needed to cover , Vertical distance =
s = u*t - 0.5*a*t^2
8.5 = v*sin(35) * (40 /  v*cos(35) ) - 0.5 * 9.8 * (40 /  v*cos(35))^2
8.5 = 40*tan(35) - 4.9 * (40 /  v*cos(35))^2

Solving for v
v = 24.47 m/s
Speed should the stream of water leave the hose , v = 24.47 m/s

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