Example8.1.15Kicking it on Mars

Some time in the recent past, Forrest traveled to Mars for a vacation with his kids, Hunter and Kelly, who wanted to kick a soccer ball around in the comparatively reduced gravity. Kelly stood at point \(K\) and kicked the ball over her dad standing at point \(F\) to Hunter standing at point \(H\text{.}\) The height of the ball off the ground, \(h\) in feet, can be modeled by the equation \(h=-0.01\left(x^2-70x-1800\right)\text{,}\) where \(x\) is how far to the right the ball is from Forrest. Note that distances to the left of Forrest will be negative.

  1. Find out how high the ball was above the ground when it passed over Forrest's head.

  2. Find the distance from Kelly to Hunter.

a coordinate plane with a dot for Kelly, Forrest and Hunter; There is an arc from Kelly to Hunter that goes over Forrest
Figure8.1.16A Soccer Kick on Mars