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

Answer:

$0 \le t \le 3$

Step-by-step 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:

$0 \le t \le 3$