Answer: 64 ft
Step-by-step explanation:
We are given the following equation that models the baseball's parabolic path:
[tex]s=16t^{2}+V_{o}t[/tex] (1)
Where:
[tex]s[/tex] is the ball maximum height
[tex]t[/tex] is the time
[tex]V_{o}=64 ft/s[/tex] is the initial height
With this information the equation is rewritten as:
[tex]s=16t^{2}+(64)t[/tex] (2)
Now, we have to find [tex]t[/tex], and this will be posible with the following formula:
[tex]V=V_{o}-gt[/tex] (3)
Where:
[tex]V=0 ft/s[/tex] is the final velocity of the ball at the point where its height is the maximum
[tex]g=32 ft/s^{2}[/tex] is the acceleration due gravity
Isolating [tex]t[/tex]:
[tex]t=\frac{V_{o}}{g}[/tex] (4)
[tex]t=\frac{64 ft/s}{32 ft/s^{2}}[/tex] (5)
[tex]t=2 s[/tex] (6)
Substituting (6) in (2):
[tex]s=16 ft/s^{2}(2 s)^{2}+(64 ft/s)(2 s)[/tex] (7)
Finally:
[tex]s=64 ft[/tex]
