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

Option D: 12.3 feet

Explanation:

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Answer 2

The maximum height of soccer ball is 12.25 ft.

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

`((-b)/(2a),f((-b)/(2a)))`

`(-b)/(2a)=(-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.