Question

Santa Claus loves to drop presents out of his sled during Christmas. The height above the ground of one present after t seconds was given by the function h(t) = -16t^2 - 20t + 800. Determine when the present was 300 feet above the ground. Determine how many seconds passed before the present hit the ground.

Answer 1

The present was 300 feet above ground 5 seconds after being thrown.

6.47 seconds passed before the present hit the ground.

Explanation:

We have the following quadratic function

`h(t) = -16t^(2) - 20t + 800`

Which determines the height of the present.

Determine when the present was 300 feet above the ground.

This is when
`h(t) = 300`. So

`h(t) = -16t^(2) - 20t + 800`

`300 = -16t^(2) - 20t + 800`

`-16t^(2) - 20t + 500 = 0`

This is
`t = -6.25` and
`t = 5`. There are no negative time instants. So the present was 300 feet above ground 5 seconds after being thrown.

Determine how many seconds passed before the present hit the ground.

This is t when
`h(t) = 0`

`h(t) = -16t^(2) - 20t + 800`

`-16t^(2) - 20t + 800 = 0`

`t = 6.47`

6.47 seconds passed before the present hit the ground.