Question

The height (ft) of an object is launched into the air given by the function h(t)=-6t^2+120t+17 where t is the time in seconds.

When will the obj reach its maximum height ?
What is the max height?
After how many seconds will it hit the ground?

Answer 1

Object will reach the max height in 10 seconds.

Max. height is 1817.

It will hit the ground in 20 seconds.

Explanation:

In order to find the x value which makes the function take its greatest value, you need to take the derivative of the function and equalize the result to 0.

h'(t)=-12t+120=0

t=10

The object will reach its maximum height in 10 seconds.

h(10) (maximum height) = 6.10.10+120.10+17= 600+1200+17=1817

Considering this is a parabola, time in total is two times more than the time passed until reaching the max. height.

10.2=20