Question

A ball is kicked upward with an initial velocity of 56 feet per second. The ball's height, h (in feet), from the ground is modeled by -16t^2+56t , where t is measured in seconds. What is the practical domain in this situation?

Answer 1

From x is greater than or equal to 0 but less than or equal to 3

Answer 2

Domain in this situation is [ 3.5 , ∞ )

Explanation:

Given:

Function is -16t² + 56t

This function gives the height, h of ball at time t.

So, h(t) = -16t² + 56t

To find : Domain of the function h(x)

We know that height of the ball can not be negative. So, put function greater than equal to 0.

⇒ h(t) ≥ 0

⇒ -16t² + 56t ≥ 0

-8t ( 2t - 7 ) ≥ 0

⇒ -8t ≥ 0

t ≥ 0

and 2t - 7 ≥ 0

2t ≥ 7

t ≥ 7/2

t ≥ 3.5

So, Domain of the function = { x : x ∈ R and x ≥ 3.5 } = [ 3.5 , ∞ )

Therefore, Domain in this situation is [ 3.5 , ∞ )