Answer:
The vertex of the parabola is found by setting the derivative of the function equal to zero and solving for t. The derivative of h(t) is h'(t) = -10t + 30. Setting this equal to zero and solving for t, we get t = 3.
Substituting t = 3 into h(t), we get h(3) = -5(3)^2 + 30(3) + 9 = 55 meters.