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A fireman, d = 50.8 m away from a burning building, directs a stream of water from a ground level fire hose at an angle of 33.3 ◦ above the horizontal. 50.8 m 44 m/s 33.3 above the horizontal.
If the speed of the stream as it leaves the hose is 44 m/s, at what height will the stream of water strike the building?
The acceleration due to gravity is 9.8 m/s 2 . Answer in units of m.

Respuesta :

Answer:

Total height at which stream can strike building is 24.02 m

Explanation:

Given data:

velocity of stream of water v = 44 m/s

Projection angle 33.3 degree

distance between fireman and building is 50.8 m

component of velocity is

[tex]v_x = vcos 33.3\ degree[/tex]

      = 44 cos 33.3 = 36.775 m/s

[tex]v_y = 44 sin 33.3  = 24.17 m/s[/tex]

time taken stream to reach building is

[tex]t =\frac{d}{v_x} = \frac{50.8}{36.77} = 1.381 sec[/tex]

Hence,  the vertical distance covered by stream in time 1.381 sec iis

[tex]s = v_y t - 0.5 gt^2[/tex]

[tex]= 24.17\times 1.38 - 0.5 \times 9.8\times 1.38^2[/tex]

s  = 24.02 m

therefore, total height at which stream can strike building is 24.02 m

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