Answer:
t = 4.875 s
h(4.875) = 686.25 ft
t ≈ 11.424 s
Step-by-step explanation:
These questions are more easily answered if the equation is written in vertex form. Subtracting the constant and dividing out -16, we get ...
h(t) -306 = -16(t^2 -9.75t)
Adding the square of half the t-coefficient inside parentheses gives ...
h(t) -306 -380.25 = -16(t^2 -9.75t +23.765625)
h(t) = -16(t -4.875)^2 + 686.25
This tells us the maximum height is 686.25 ft at time t = 4.875 seconds.
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When the rock hits the ground, h(t) = 0, so ...
0 = -16(t -4.875)^2 + 686.25
686.25/16 = (t -4.875)^2 . . . . . subtract 686.25, divide by -16
√42.890625 +4.875 = t ≈ 11.424 . . . . take the square root, add 4.875
The rock hits the ground after about 11.424 seconds.
