#Script to support Exercise 2.2.9, modeling shuttlecock data.

#Times at which position was measured (seconds)
times = [0, 0.347, 0.47, 0.519, 0.582, 0.65, 0.674, 0.717, 0.766, 0.823, 0.87, 1.031, 1.193, 1.354, 1.501, 1.726,
1.873];

#Distance fallen (meters)
data = [0, 0.61, 1.00, 1.22, 1.52, 1.83, 2.00, 2.13, 2.44, 2.74, 3.00, 4.00, 5.00, 6.00, 7.00, 8.50, 9.50];

#Plot the raw data versus time. Call the plot "plot1".
pdata = list(zip(times,data))
plt1 = scatter_plot(pdata)
plt1.axes_labels(['time (seconds)','Distance (meters)'])
show(plt1)

#Now use g = 9.8, take a guess at k (k=1 is a good start), plot d(t) from part (b), and compare to the data.