Suppose you measured the speed of a falling shuttlecock and got the following data points.

a. Use a Riemann sum to approximate the total distance travelled by the shuttlecock.
Use whichever Riemann sum you want.

b. Use the trapezoid rule to approximate the total distance travelled by the shuttlecock.

c. Use the central difference formula to approximate the of the shuttlecock when t = 0.75 s.

d. A model of the shuttlecock’s velocity is v = vmax(1−e −kt).
Use the table to suggest an appropriate value for vmax, the terminal velocity. (Hint: What is limt→∞ vmax(1 − e −kt)?)

e. Plot the points and the curve to verify that they are in good agreement when k = 3/s.

f. Use the equation in part

(d) to calculate the acceleration when t = 0.75 s.
g. Use the equation in part

(d) to calculate the total distance travelled between 0 and 2 seconds.