Question

A brush fire is burning on a rock ledge on one side of a ravine that is 20 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.
At what speed should the stream of water leave the hose so that the water hits the fire on the first shot?

Answer 1

s = that speed

u = s cos 35 = .819 s
Vi = s sin 35 = .574 s

20 = u t
so t = 20/u = 20/.819 s = 24.4/s

h = 6.5 = Vi t -4.9 t^2

6.5 = .574 s (24.4/s) - 4.9 (24.4/s)^2

6.5 = 14 - 2917 /s^2

2917 = 7.5 s^2

s = 19.7 m/s

Answer 2

Damon's response is almost correct. Because the fire is 6.5m lower than the hose, you have to use -6.5 instead of 6.5 in the "h =" part. It causes the answer to end up being around 12 m/s instead.