Chapter 8.4, Problem 55PE

A ball is kicked off the side of a hill at an angle of elevation of $30°.$ The hill slopes downward $30°$ from the horizontal. Consider a coordinate system in which the origin is the point on the edge of the hill from which the ball is kicked. The path of the ball and the line of declination of the hill can be approximated by

$\begin{array}{l}y=-\frac{x^2}{192}+\frac{\sqrt{3}}{3}x\text{Path of the ball}\\ y=-\frac{\sqrt{3}}{3}x\text{Line of declination of the hill}\end{array}$

Solve the system to determine where the ball will hit the ground.