A fireman,50.4 m away from a burning building,directs a stream of water from a fire hose at an angle of 31.2° above the horizontal.If the initial speed of the stream is 46.8 m/s,at what height will the stream of water strike the building?

A) 42.6 m
B) 9.3 m
C) 22.8 m
D) 29.2 m
E) 27.9 m

Question

A fireman,50.4 m away from a burning building,directs a stream of water from a fire hose at an angle of 31.2° above the horizontal.If the initial speed of the stream is 46.8 m/s,at what height will the stream of water strike the building?
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A) 42.6 m
B) 9.3 m
C) 22.8 m
D) 29.2 m
E) 27.9 m

Quizplus · Accepted Answer

First, we need to split the initial velocity of the stream into horizontal and vertical components.

Horizontal component: 
v_x = v cos(θ) 
v_x = (46.8 m/s) cos(31.2°) 
v_x = 40.12 m/s

Vertical component: 
v_y = v sin(θ) 
v_y = (46.8 m/s) sin(31.2°) 
v_y = 23.30 m/s

Now, we can use the vertical component and the equation for projectile motion to find the height at which the stream strikes the building:

y = y_0 + v_y*t - 0.5*g*t^2

where: 
y_0 = 0 (we can set the ground level as the reference point) 
v_y = 23.30 m/s 
g = 9.81 m/s^2 (acceleration due to gravity)

To find the time it takes for the stream to reach the building, we need to use the horizontal component:

x = v_x*t 
t = x/v_x 
t = 50.4 m / 40.12 m/s 
t = 1.256 s

Now we can substitute this time into the previous equation:

y = 0 + (23.30 m/s)(1.256 s) - 0.5(9.81 m/s^2)(1.256 s)^2 
y = 22.8 m

Therefore, the stream of water will strike the building at a height of 22.8 m.

A Fireman,50