Answer:
The maximum height of soccer ball is 12.25 ft.
Step-by-step explanation:
It is given that Tiffany kicks a soccer ball off the ground and in the air, with an initial velocity of 28 feet per second. It means v = 28 ft.
Given formula is
[tex]H(t)=-16t^2+vt+s[/tex]
The initial height of ball is 0.
[tex]H(0)=-16(0)^2+v(0)+s[/tex]
[tex]0=s[/tex]
The height of ball defined by the function
[tex]H(t)=-16t^2+(28)t+0[/tex]
[tex]H(t)=-16t^2+28t[/tex]
It is a downward parabola and the vertex of a downward parabola is the point of maxima.
The vertex of a parabola [tex]f(x)=ax^2+bx+c[/tex] is
[tex](\frac{-b}{2a},f(\frac{-b}{2a}))[/tex]
[tex]\frac{-b}{2a}=\frac{-28}{2(-16)}=0.875[/tex]
[tex]H(0.875)=-16(0.875)^2+28(0.875)=12.25[/tex]
Therefore the maximum height of soccer ball is 12.25 ft.
