Question

A swimmer takes a running jump off a pier. The path of the swimmer can be modeled by the equation h=-0.1d^2+0.1d+3, where h is the height (in feet) and d is the horizontal distance (in feet). How far from the pier does the swimmer enter the water?

Answer 1

6 feet from the pier

Explanation:

The path of the swimmer can be modeled by the equation

`h=-0.1d^2+0.1d+3,`

where h is the height (in feet) and d is the horizontal distance (in feet).

Find d, when h is equal to 0 (when the swimmer enters the water):

`-0.1d^2+0.1d+3=0\\ \\-d^2+d+30=0\ \ [\text{Multiply by 10}]\\ \\d^2-d-30=0\ \ [\text{Multiply by -1}]\\ \\d^2-6d+5d-30=0\\ \\d(d-6)+5(d-6)=0\\ \\(d-6)(d+5)=0\\ \\d-6=0\ \text{or}\ d+5=0\\ \\d=6\ \text{or}\ d=-5`

The distance cannot be negative, so

`d=6` feet