Question 214441
Find the maximum height:
{{{h(t) = -4.9t^2+6t+0.6}}}
First find the time t, at which the ball reaches its maximum height.
This can be found by noting that the curve described by this quadratic equation (this is necessarily the trajectory of the ball) is a parabola that open downward.  The maxumum point on this parabola occurs at the vertex of the parabola.
The x-coordinate (t-coordinate in this problem) is found by:
{{{t = -b/2a}}} where, from the given equation, a = -4.9 and b = 6.
{{{t = -6/2(-4.9)}}}
{{{t = 0.6122}}}seconds. Now substitute this value of t into the given equation and solve for {{{h[m]}}}, the maximum height.
{{{h[m](0.6122) = -4.9(0.6122)^2+6(0.6122)+0.6}}}
{{{h[m](0.6122) = 2.43}}}meters.
The maximum height of the ball is 2.4 meters.