Question

A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds,

is given by h(t) = -4.9t? + 16 + 13. How long does it take to reach maximum height? (Round your answer to three
decimal places.)

S=?

Answer 1

It takes 1.633 seconds for the ball to reach maximum height.

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), f(x_(v))`

In which

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

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

In this question:

We have that the height is given by:

`h(t) = -4.9t^2 + 16t + 13`

So
`a = -4.9, b = 16, c = 13`.

The maximum height happens at the instant of time:

`t_v = -(b)/(2a) = -(16)/(2(-4.9)) = (16)/(9.8) = 1.633`

It takes 1.633 seconds for the ball to reach maximum height.