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

Answer:

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

Step-by-step 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

$x_{v} = -\frac{b}{2a}$

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:

$t_v = -\frac{b}{2a} = -\frac{16}{2(-4.9)} = \frac{16}{9.8} = 1.633$

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