To find the maximum height, we need to determine the vertex of the parabolic function h(t) = -16t^2 + 96t + 60. The vertex of a parabola is the highest or lowest point on the curve.
The formula for the x-coordinate of the vertex of a parabola in the form ax^2 + bx + c is given by x = -b / (2a).
In this case, a = -16 and b = 96. Plugging these values into the formula, we get:
x = -96 / (2 * -16) = -96 / (-32) = 3
So, the rocket reaches its maximum height at t = 3 seconds.
To find the maximum height, we substitute t = 3 into the equation h(t) = -16t^2 + 96t + 60:
h(3) = -16(3)^2 + 96(3) + 60 = -16(9) + 288 + 60 = -144 + 288 + 60 = 204
Therefore, the rocket reaches a maximum height of 204 feet.