Question

The function h(t)=-16t^+144 represents the height, h(t), in feet of an object from the ground at t seconds after it is dropped. A realistic domain for this function is?

Answer 1

`0 \le t \le 3`

Explanation:

Given

`h(t) = -16t^2 + 144`

Required

Determine a reasonable domain

The domain is the possible values of t for which h(t) is true

Before the object is released, the value of t is:

`t = 0`

Next, is to calculate the value of t after the ball reaches the ground.

At this point, h = 0.

So, we have:

`h(t) = -16t^2 + 144`

`0 = -16t^2 + 144`

`16t^2 = 144`

Divide both sides by 16

`t^2 = 9`

Take the positive square root of both sides

`t = 3`

This means that the ball reaches the ground in 3 seconds.

So, the domain is:

`0 \le t \le 3`