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 2 + 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

The rock will hit the ground when y=0, so we need to solve this equation for its roots. To do that, we set it equal to 0:

`0=-0.005x^(2)+0.41x-5.1`

Divide everything by -0.005 to clear out the decimals:

`0=x^(2)-82x+1020`

Now use the quadratic formula:

`x=(82 \pm √(82^2-4*1020))/(2)`

`x=15.29` or
`x=66.71`
We want the larger x value since the smaller one is when the rock will reach the top of the hole.