The ball will take approximately 0.39 seconds to reach maximum height.
In this question we are going to determine the maximum height based on the characteristics inherent to second order polynomials and the quadratic formula.
Mathematically speaking, the function height of the ball represents a parabola, whose vertex represents an absolute maximum. In order to find the time needed for the ball we need to rearrange the given quadratic function:
[tex]-4.9\cdot t^{2} +3.82\cdot t + (1.7-h) =0[/tex] (1)
The quadratic formula of the equation is:
[tex]t = \frac{-3.82\pm \sqrt{3.82^{2}-4\cdot (-4.9)\cdot(1.7-h)}}{2\cdot (-4.9)}[/tex]
The discriminant must be zero in order to determine the time needed to reach maximum height:
[tex]t = -\frac{3.82}{2\cdot (-4.9)} \,s[/tex]
[tex]t \approx 0,390\,s[/tex]
The ball will take approximately 0.39 seconds to reach maximum height.
We kindly invite to see this question on parabolae: https://brainly.com/question/12793264
