Answer:
[tex]0 \le t \le 3[/tex]
Step-by-step explanation:
Given
[tex]h(t) = -16t^2 + 144[/tex]
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:
[tex]t = 0[/tex]
Next, is to calculate the value of t after the ball reaches the ground.
At this point, h = 0.
So, we have:
[tex]h(t) = -16t^2 + 144[/tex]
[tex]0 = -16t^2 + 144[/tex]
[tex]16t^2 = 144[/tex]
Divide both sides by 16
[tex]t^2 = 9[/tex]
Take the positive square root of both sides
[tex]t = 3[/tex]
This means that the ball reaches the ground in 3 seconds.
So, the domain is:
[tex]0 \le t \le 3[/tex]
