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) = -4.9t² + 18t + 0. how many seconds does it take to reach maximum height? enter the answer with at least 3 decimal places.

Explanation:

Step1: Identify the quadratic function form

The height function is \(h(t)=-4.9t^{2}+18t + 6\). For a quadratic function \(y = ax^{2}+bx + c\), the time \(t\) at which the vertex (maximum for \(a<0\)) occurs is given by \(t=-\frac{b}{2a}\). Here \(a=-4.9\) and \(b = 18\).

Step2: Calculate the time \(t\)

Substitute \(a=-4.9\) and \(b = 18\) into the formula \(t=-\frac{b}{2a}\).

$$t=-\frac{18}{2\times(-4.9)}=\frac{18}{9.8}\approx1.837$$

Answer:

\(1.837\)