Answer:
0.5 seconds (at 100 feet in the air).
Step-by-step explanation:
So, the height of the ball can be modeled by the function:
Where h(t) represents the height in feet after t seconds.
And we want to find its maximum height.
Notice that our function is a quadratic.
Therefore, the maximum height will occur at the vertex of our function.
The vertex of a quadratic function in standard form is given by the formula:
In our function, a=-16; b=16; and c=96.
Find the x-coordinate of the vertex:
So, the ball reaches its maximum height after 0.5 seconds of its projection.
Notes:
To find it’s maximum height, we can substitute 1/2 for our function and evaluate. So:
Evaluate:
So, the ball reaches its maximum height of 100 feet 0.5 seconds after its projection.