A fireman, 57.6 m away from a burning building, directs a stream of water from a

Question

A fireman, 57.6 m away from a burning building, directs a stream of water from a fire hose at an angle of 35.2 degrees above the horizontal. If the initial speed of the stream is 42.7 m/s. a) At what height will the stream of water strike the building? b) What is the velocity of the stream as it hits the building (give both magnitude and direction)? c) Despite the fireman’s best effort to put the fire out, the building continues to burn with even more intensity forcing the fireman to move away from the building. Assuming the initial speed of the stream and angle at which the hose is directed at the building remains the same (as given above), can the fireman move further away from the building and still strike the building at the same height found in part a and if so how far away from the building can he stand? A fireman, 57.6 m away from a burning building, directs a stream of water from a fire hose at an angle of 35.2 degrees above the horizontal. If the initial speed of the stream is 42.7 m/s. a) At what height will the stream of water strike the building? b) What is the velocity of the stream as it hits the building (give both magnitude and direction)? c) Despite the fireman’s best effort to put the fire out, the building continues to burn with even more intensity forcing the fireman to move away from the building. Assuming the initial speed of the stream and angle at which the hose is directed at the building remains the same (as given above), can the fireman move further away from the building and still strike the building at the same height found in part a and if so how far away from the building can he stand? a) At what height will the stream of water strike the building? b) What is the velocity of the stream as it hits the building (give both magnitude and direction)? c) Despite the fireman’s best effort to put the fire out, the building continues to burn with even more intensity forcing the fireman to move away from the building. Assuming the initial speed of the stream and angle at which the hose is directed at the building remains the same (as given above), can the fireman move further away from the building and still strike the building at the same height found in part a and if so how far away from the building can he stand?

Explanation / Answer

Given,

D = 57.6 m ; theta = 35.2 deg ; Vi = 42.7 m/s

Vix = 42.7 x cos35.2 = 34.9 m/s

Viy = 42.7 x sin35.2 = 24.6 m/s

D = Vix t => t = 57.6/34.9 = 1.65 s

we know that

S = ut + 1/2 at^2

H = 24.6 x 1.65 - 0.5 x 9.8 x 1.65^2 = 27.25 m

Hence, H = 27.25 m

b)we know that

v = u + at

Viy' = 24.6 - 9.8 x 1.65 = 8.43 m/s

V = sqrt (34.9^2 + 8.43^2) = 35.9 m/s

Hence, V = 35.9 m/s

b)As he moves away the distance D increases, and the time t will also increase,

So the height will reduce and he can not strike the building at the same point.

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