Question

Reba kicks a soccer ball off the ground and in the air, with an initial velocity of 25 feet per second. Using formula H(t) = - 1612 + vt + s, what is the maximum height the soccer ball reaches?. Using the formula HC -1662 + vt +s, what is the maximum height the soccer ball reaches? ​

Answer 1

The maximum height the soccer ball reaches is 9.77 feet.

Explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

`f(x) = ax^(2) + bx + c`

It's vertex is the point
`(x_(v), y_(v))`

In which

`x_(v) = -(b)/(2a)`

`y_(v) = -(\Delta)/(4a)`

Where

`\Delta = b^2-4ac`

If a<0, the vertex is a maximum point, that is, the maximum value happens at
`x_(v)`, and it's value is
`y_(v)`.

Reba kicks a soccer ball off the ground and in the air, with an initial velocity of 25 feet per second.

The formula for the height is:

`h(t) = -16t^2 + v(0)t + h(0)`

In which v(0) is the initial velocity and s(0) is the initial height.

Initial velocity of 25 feet per second means that
`v(0) = 25`

Kicked off the ground means that
`h(0) = 0`. So

`h(t) = -16t^2 + 25t`

Which is a quadratic equation with
`a = -16, b = 25, c = 0`.

The maximum value is:

`y_(v) = -(\Delta)/(4a)`

In which

`\Delta = b^2-4ac = 25^2 - 4(-16)(0) = 625`

`y_(v) = -(\Delta)/(4a) = (625)/(4(16)) = 9.77`

The maximum height the soccer ball reaches is 9.77 feet.