Question

Landon is standing in a hole that is 5.1 ft deep. He throws a rock, and it goes up into the air, out of the hole, and then lands on the ground above. The path of the rock can be modeled by the equation y = 0.005x + 0.41x 5.1, where x is the horizontal distance of the rock, in feet, from Landon and y is the height, in feet, of the rock above the ground. How far horizontally from Landon will the rock land?

Answer 1

We can model the path of the stone as shown in the diagram below. The horizontal distance is shown between the two point on the x-axis which values we can find by solving the quadratic equation

$0.005x^{2}+0.41x+5.1=0$

The easiest method to use is the Quadratic Formula
$x_{1,2}= \frac{-b+\sqrt{ b^{2}-4ac} }{2a}$

$a=0.005$
$b=0.41$
$c=5.1$

Substitute a, b, and c into the formula, we obtain $x=40.3$ and $x=-122.3$ and the distance in between is 162.6 ft