Chapter 5.1, Problem 36E

Free fall Use geometry and the figure given in Exercise 35 to estimate how far Felix fell in the first 20 seconds of his free fall.

Free fall On October 14, 2012, Felix Baumgartner stepped off a balloor capsule at an attitude of a most 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 x₀ – 34, x₁ – 40, x₂ – 46, x₃ – 52, x₄ – 58, and x₃ = 64. Use left and right Riemann sums to estimate how far Felix fall while travelling at supersonic speed.

  b.    It is claimed that the actual distance that Felix fell at supersonic speed was approximately 10.495 m. Which estimate in part (a) produced the more accurate estimate?

  c.    How could you obtain more accurate estimates of the total distance fallen than those found in part(a)?