Answer:
The maximum height of ball is 18.1 feet. Option 2 is correct.
Step-by-step explanation:
The height of the soccer ball is defined by the formula,
\(h(t)=-16t^2+vt+s\)
Where, v is initial velocity and s is initial height of ball.
It is given that initial velocity is 34 feet per second and the initial height of ball is 0.
\(h(t)=-16t^2+34t\)
The leading coefficient is negative, so it is a downward parabola. The vertex of a downward parabola is point of maxima.
The vertex of a parabola \(f(x)=ax^2+bx+c\) is
\((\frac{-b}{2a},f(\frac{-b}{2a}))\)
\(\frac{-b}{2a}=\frac{-34}{2(-16)}=1.0625\)
\(h(1.0625)=-16(1.0625)^2+34(1.0625)=18.0625\approx 18.1\)
Therefore the maximum height of ball is 18.1 feet. Option 2 is correct.
