To solve this problem, we need the equation that models the height of the ball as a function of time, which I assume is missing in your statement. Typically, the height function for an object thrown upward is quadratic and follows this form:

$h(t) = -at^2 + bt + c$

where:

• $a$ is the coefficient related to gravity,
• $b$ is the initial velocity,
• $c$ is the initial height of the ball.

To find the time it takes to reach the maximum height, we use the fact that the maximum height occurs at the vertex of the parabola described by the quadratic equation. The time at which the vertex occurs is given by the formula:

$t_{\text{max}} = \frac{-b}{2a}$

If you provide the equation for the height function $h(t)$, I can apply this formula to determine the time at which the ball reaches its maximum height.

Would you like to provide the equation or clarify it?