Answer:
The ball will reach its maximum height at 2 seconds after being launched
Step-by-step explanation:
Vertical Launch
The height of a ball thrown into the air is given by
[tex]f (t) = -16t^2 + 64t + 960[/tex]
Where t is the time in seconds after the ball was released. We want to find the time when the ball reaches a maximum point, i.e. the time that makes [tex]f(t_m) = maximum[/tex]. The equation of f(t) is a parabola which is known for having a vertex located at the point
[tex]\displaystyle t=-\frac{b}{2a}[/tex]
where a and b are given by the general formula of the parabola
[tex]f(t)=at^2+bt+c[/tex]
For our ball, the time needed to reach the maximum height is
[tex]\displaystyle t=-\frac{64}{2(-16)}=2\ sec[/tex]
The ball will reach its maximum height at 2 seconds after being launched
