The given function for the height of the ball is:

$h(t) = 100 - 16t^2$

Here, $t$ represents the time in seconds, and $h(t)$ is the height of the ball at time $t$.

To find the time it will take for the ball to reach a specific height $h$, we need to solve for $t$ in terms of $h$. Let's rewrite the equation to express $t$ as a function of $h$.

Step 1: Set up the equation for $h$:

$h = 100 - 16t^2$

Step 2: Solve for $t^2$:

Subtract 100 from both sides:

$h - 100 = -16t^2$

Now, divide both sides by -16:

$t^2 = \frac{100 - h}{16}$

Step 3: Solve for $t$:

Take the square root of both sides:

$t = \pm \sqrt{\frac{100 - h}{16}}$

Since time $t$ must be non-negative, we only take the positive root:

$t = \sqrt{\frac{100 - h}{16}}$

Final Function:

The function that gives the time $t$ when the ball reaches a height $h$ is:

$t(h) = \sqrt{\frac{100 - h}{16}}$

Would you like further details or examples for how to use this function?

Here are 5 related questions to think about:

1. How long will it take for the ball to reach a height of 50 feet?
2. What is the maximum height the ball can reach after being dropped?
3. At what time will the ball hit the ground (i.e., $h = 0$)?
4. What happens to the function if the ball is dropped from a different height?
5. How would the equation change if gravity had a different constant?

Tip: When solving quadratic equations, always check if taking the square root introduces any positive-negative ambiguity in the solution!