Question 214441
h(t) = -4.9t^2+6t+0.6
.
Because of the negative coefficient associated with the t^2, we know that it is a parabola cup down.  This means that if we find the "vertex" we will have the maximum.
.
The "axis of symmetry" is at:
-b/(2a)
= -6/(2*(-4.9))
= -6/(2*(-4.9))
= 0.612 seconds
This is the time it takes to reach the peak.
.
To find the height, plug the above back into:
h(t) = -4.9t^2+6t+0.6
h(0.612) = -4.9(0.612)^2+6(0.612)+0.6
h(0.612) = 2.4 meters