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 4.5 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?

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aristocles aristocles · Answer 1 · 2019-11-15T02:50:29+01:00

Answer:

[tex]v_o = 30.5 m/s[/tex]

Explanation:

Height of the hose pipe is given as

[tex]y = 4.5 m[/tex]

horizontal distance is given as

[tex]x = 25 m[/tex]

angle of elevation is given as 35 degree with the horizontal

now we know that the horizontal distance moved is given as

[tex]x = (v_ocos35) t[/tex]

[tex]y = 4.5 + (v_o sin35) t - \frac{1}{2}(9.8)t^2[/tex]

now we have

[tex]25 = v_o(0.82)t[/tex]

also we have

[tex]0 = 4.5 + 0.57 v_o t - 4.9 t^2[/tex]

[tex]0 = 4.5 + (0.57)(0.82) - 4.9 t^2[/tex]

[tex]t = 1.00 s[/tex]

so we have

[tex]v_o = 30.5 m/s[/tex]