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

Answer:

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

6.47 seconds passed before the present hit the ground.

Step-by-step 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.