35. Free fall On October 14, 2012, Felix Baumgartner stepped off a balloon capsule at an altitude of almost 39 km above Earth's surface and began his free fall. His velocity in m/s during the fall is given in the figure. It is claimed that Felix reached the speed of sound 34 seconds into his fall and that he continued to fall at supersonic speed for 30 seconds. (Source: http://www.redbullstratos.com) a. Divide the interval [34, 64] into n = 5 subintervals with the gridpoints x = 34, x *5 = 40, X2 = 46, x3 = 52, x = 58, and 46,X3 X4 = 64. Use left and right Riemann sums to estimate how far Felix fell while traveling at supersonic speed. b. It is claimed that the actual distance that Felix fell at super- sonic speed was approximately 10,485 m. Which estimate in part (a) produced the more accurate estimate? c. How could you obtain more accurate estimates of the total dis- tance fallen than those found in part (a)? VA 400 300 200 100 0 10 20 30 40 50 60 70 80 36. Free fall Use geometry and the figure given in Exercise 35 to esti- mate how far Felix fell in the first 20 seconds of his free fall.