Question

The height of a free falling object at time t can be found using the function, h(t) = - 12t2 + 36t. Where h(t) is the height in feet and t is the in seconds. Find the time when the object hits the ground

Answer 1

3 seconds is the time when the object hits the ground.

Explanation:

Given the height of a free falling object at time t can be found using the function is given by:

`h(t)=-12t^2+36t` ....[1]

where,

h(t) is the height in feet

t is the in seconds.

We have to find the time when the object hits the ground.

⇒h(t) = 0

Substitute this in [1] we have;

`-12t^2+36t =0`

⇒
`12t^2-36t = 0`

⇒
`12t(t-3) = 0`

⇒t = 0 and t = 3

Since, time cannot be 0.

⇒t = 3 seconds

Therefore, the time when the object hits the ground is, 3 seconds

Answer 2

For this case we have the following equation:
h (t) = - 12t2 + 36t
When the object hits the ground we have:
- 12t2 + 36t = 0
We look for the roots of the polynomial:
t1 = 0
t2 = 3
Therefore, the time it takes the object to hit the ground is:
t = 3 s
Answer:
the time when the object hits the ground is:
t = 3 s