Question

Tiffany kicks a soccer ball off the ground and in the air, with an initial velocity of 28 feet per second. Using the formula H(t) = −16t2 + vt + s, what is the maximum height the soccer ball reaches?

Answer 1

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

$H(t)=-16t^2+vt+s$

The initial height of ball is 0.

$H(0)=-16(0)^2+v(0)+s$

$0=s$

The height of ball defined by the function

$H(t)=-16t^2+(28)t+0$

$H(t)=-16t^2+28t$

It is a downward parabola and the vertex of a downward parabola is the point of maxima.

The vertex of a parabola $f(x)=ax^2+bx+c$ is

$(\frac{-b}{2a},f(\frac{-b}{2a}))$

$\frac{-b}{2a}=\frac{-28}{2(-16)}=0.875$

$H(0.875)=-16(0.875)^2+28(0.875)=12.25$

Therefore the maximum height of soccer ball  is 12.25 ft.