SOLUTION: Water issuing from the end of a horizontal pipe 30 ft. above the ground describes a parabolic curve, where the vertex is at the end of the pipe. At a point 10 ft. below the pipe, t

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Water issuing from the end of a horizontal pipe 30 ft. above the ground describes a parabolic curve, where the vertex is at the end of the pipe. At a point 10 ft. below the pipe, t      Log On


   

Question 1019411: Water issuing from the end of a horizontal pipe 30 ft. above the ground describes a parabolic curve, where the vertex is at the end of the pipe. At a point 10 ft. below the pipe, the water is 12 ft. from the vertical line through the end of the pipe. How far from this vertical line will the water strike the ground? (Show your drawing)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Standard Form equation for a parabola, y=a%28x-h%29%5E2%2Bk.

Water issuing from the end of a horizontal pipe 30 ft. above the ground describes a parabolic curve, where the vertex is at the end of the pipe.
y=a%28x-0%29%5E2%2B30

At a point 10 ft. below the pipe, the water is 12 ft. from the vertical line through the end of the pipe.
30-10=a%2812-0%29%5E2%2B30
20=144a%2B30
144a=-10
a=-10%2F144
a=-5%2F72

highlight%28highlight_green%28y=-%285%2F72%29x%5E2%2B30%29%29

The question means, find x for y=0.

A graph of this could be either the left branch or the right branch of the parabola, to correspond with the representation of the situation for the end of the hose being the vertex (a maximum point). The equation is done in standard form, so easier to graph.
graph%28300%2C300%2C-30%2C30%2C-10%2C50%2C-%285%2F72%29x%5E2%2B30%29