Question

A fire hose ejects a stream of water at an angle of 31.7 ° above the horizontal. The water leaves the nozzle with a speed of 29.2 m/s. Assuming that the water behaves like a projectile, how far from a building should the fire hose be located to hit the highest possible fire?

Answer 1

Vi=29.2 m/s
θ=31.7°
Vxi=Vi cos(θ) = 24.844 m/s
Vyi=Vi sin(θ) = 15.344 m/s
since
Vy(t)=Vyi-gt
so at the maximum,
Vy(t)=0, or Vyi-gt=0
=>
t=Vyi/g
The optimal (best) horizontal distance would therefore be the horizontal distance travelled during this time interval, or
X = (Vyi/g)*Vxi
(for checking: 35<X<40 m)