Imagine an engineer is monitoring the height of a drone above the ground as it flies a pre-programmed path. The height, h, in meters, of the drone can be modeled using the function h = 15cos(πt/120) + 18, where t is the time, in seconds.
a) Determine the average rate of change of h in the following time intervals, rounded to three decimal places.
i) 15s to 20s
ii) 19s to 20s
iii) 19.9s to 20s
iv) 19.99s to 20s
b) Estimate a value for the instantaneous rate of change of h at t=20s.
c) What physical quantity does this instantaneous rate of change represent?
d) Would you expect the instantaneous rate of change of h to be the same at t=25s? Justify your answer.
