Question

a fire hose is held near the ground shoots water at a speed of 6.5m/s. at what angle(s) should the nozle point in order that the water land 2.0 m away? why are there two different angles?

Answer 1

\[L=\frac{v_0^2}{g}\sin{2\alpha}\quad(g\approx 10m/s^2)\]\[\sin{2\alpha}=\frac{gL}{v_0^2}\approx 0.473\]\[\alpha_1=\frac{1}{2}\arcsin{0.473}=14.1^\circ\quad\vee\quad\alpha_2=\frac{1}{2}(180^{\circ}-\arcsin{0.473})=75.9^\circ\]

Answer 2

\[L(\alpha)=\frac{2v_0^2}{g}\sin\alpha\cos\alpha\]\[\beta=90^\circ-\alpha\]\[L(\beta)=\frac{2v_0^2}{g}\sin\beta\cos\beta=\frac{2v_0^2}{g}\sin{(90^\circ-\alpha)}\cos{(90^\circ-\alpha)}=\]\[=\frac{2v_0^2}{g}\cos\alpha\sin\alpha=L(\alpha)\]

Answer 3

i dont understand..