Answer:
124 feet
Step-by-step explanation:
See attachment.
At t = 0 minutes, the coaster is 60 feet off the group. At t=2 minutes, it is 124 feet high, just before the plunge.
We could also take the first derivative and set it equal to zero. The first derivative gives us the slope of the line at any point t. The slope is zero at the top, just before the screams kick in.
h(t) = -16t^2 + 64t + 60
h'(t) = -32t + 64
0 = -32t + 64
32t = 64
t = 2
The top is reached in 2 minutes. Use t = 2 in the equation to find height:
h(2) = -16(2)^2 + 64*(2) + 60
h(2) = -64 + 128 + 60
h(2) = 124 feet
