A brush fire is burning on a rock ledge on one side of a ravine that is 25 m wid

Question

A brush fire is burning on a rock ledge on one side of a ravine that is 25 m wide. A fire truck sits on the opposite side of the ravine at an elevation 6.5 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.

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

Explanation / Answer

ux = u cos(35) =0.819 u

uy = usin(35) = 0.574 u

ALong horizontal direction

d = ux*t

25 = 0.819 u*t

t = 30.525 /u

From kinematic equaiton along verticla direction

h =uyt+(1/2)ayt2

6.5 = (0.574u)*(30.525/u) -(1/2)(9.8)(30.525/u)^2

u =20.35 m/s

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