6) Consider a ball thrown at an angle 9 above the horizontal ground with an initial speed vo in a medium with linear drag. Consider a particular case where vo = vter and ver/9 = 1. We know that in vacuum the maximum range is at 8 = 7/4. Determine the maximum range (and angle) when we include linear air resistance: a Plot Eq.2.37) in Taylor for different values of 0 and try by inspection to figure out the angle at which the range is maximum. (With the assumptions above, most unit-full quantities become "one", but do be careful of the fact that e.g. 00. is vo cos(6), not vo). b Use a root finder to find the range when 0 = */4. Any root finder will require you to make a guess for the root. This is what is called the "neighborhood of the root" or "bracketing the root". A screen- cast showing how to use Mathematica to find roots is available here: http://youtu.be/6731Q6Z-6Yc c Repeat for different values of # (homing in on a small range near the angle you estimated in part a). Contime until you know the maximum range to 3 significant digits and the corresponding angle to two significant figures. Connect to point a) and compare with the ideal vacuum values. Briefly, discuss