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Homework Statement
A parent takes their child to a water slide which is shaped similar to a portion of a parabola (see diagram). There is an elevator 3m from the edge of the pool. The elevator takes the rider to the top of the slide which is 19m above ground. The rider slides down and falls into pool from height of 1m. The parent (he is 2m tall) is standing 1m from the elevator and wishes to take a picture of the child when they are closest to the parent. What is the MIN. distance between parent and child?
The Attempt at a Solution
I sketched out the diagram attached. I know that the yaxis represents the the height that he started at; (0,19). I believe at the very edge of the slide is the vertex, and in this case (9.5,1). Based on symmetry, the parabola would also have (19,19) as a point.
But now I am stuck. I don't know what strategy to pursue in order to obtain this minimum distance.
EDIT: I know eqs:
s(t) = 0.199x^2  3.79x + 19
v(t) = s'(t) = 0.398x  3.79
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