CM PS #14: Taylor 9.19, 9.21, 9.24

  • Taylor problems 9.19, 9.21, and 9.24 (along with 9.20, which is not assigned but is the source of the trajectory equations used in 9.24; while you don’t need to solve problem 9.20, you will need to look at it to understand the trajectory equations you plot in 9.24) form a nice set.
  • Treat problems 9.19, 9.21, and 9.24 as one problem.
  • You may use the results of problem 9.24 for the sketches/descriptions of the motions described in 9.19 and 9.21, but make sure to explain those motions in terms of the forces (standard and frame-dependent), as requested in those problems.
  • Make sure you identify which of the plots from problem 9.24 correspond to which situations from 9.19 and 9.21.
  • In addition to the standard plotting window (I recommend plotting from 0 < t < 5), also make sure to present plots that zoom in on any interesting features.
  • Two of the graphs will look identical at first glance. Zoom in further and further on the initial trajectory until any differences become apparent.
  • You are encouraged to use MMA or Desmos or other plotting program to make your plots, and it would be great if you started from scratch using documentation. However, for your convenience, I quickly built a no-frills Desmos that you may start from/modify. In that Desmos, I used vx0 = 0.6 and vy0 = 0.8 so that it would be easier to identify the trajectory equations in the Desmos syntax. Here’s a link to that no-frills Desmos: https://www.desmos.com/calculator/9c5s0dniun.