Given,
The initial height of the soccer ball, h₁=6 ft
The initial velocity of the ball, u=96 ft/s
The acceleration due to gravity, g=-32 ft/s
When the ball reaches the maximum height, its velocity will reduce to zero.
Thus the velocity of the ball when it is at its maximum height is v=0 ft/s
From the equation of motion,
[tex]v^2-u^2=2gh_2[/tex]
Where h₂ is the total height covered by the ball from its initial height to reach its maximum height.
On substituting the known values,
[tex]\begin{gathered} 0-96^2=2\times-32\times h_2 \\ \Rightarrow h_2=\frac{-96^2}{2\times-32} \\ =144\text{ ft} \end{gathered}[/tex]
Thus the maximum height reached by the ball is,
[tex]\begin{gathered} H=h_1+h_2 \\ =6+144 \\ =150\text{ ft} \end{gathered}[/tex]
Thus the maximum height reached by the ball is 150 ft.
