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Question 624116: water sprouts (the curve described by the water stream, assumed to be a parabola) from a horizontal pipe 40 feet above the ground. twenty feet below theline of the pipe, the water stream is at a horizontal distanceof 16 feet from the vertical line through the end of the pipe. how far from the vertical line will the stream of water hit the ground?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! water sprouts (the curve described by the water stream, assumed to be a parabola) from a horizontal pipe 40 feet above the ground. twenty feet below theline of the pipe, the water stream is at a horizontal distanceof 16 feet from the vertical line through the end of the pipe. how far from the vertical line will the stream of water hit the ground?
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We are working with a parabola that opens downwards with vertex at (0,0)
Form of equation: y=Ax^2
A horizontal distance of 16 ft from the vertical line and 20 ft below the line gives you a point of (16,-20) on the parabola.
Solving for A, using these coordinates:
-20=A16^2
A=-20/256
A=-0.078125
Equation of parabola:
y=-.078125x^2
when water hits the ground, y=-40
-40=-.078125x^2
x^2=40/.078125
x^2=512
x=√512≈22.63 ft
The stream of water will hit the ground 22.63 ft from the vertical line.
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