A Brief Look at the Force of Drag using Numerical Modeling (or The Euler Method)
(22:00)
This is how you include air resistance in projectile motion.  It requires the Drag Force and Numerical Modeling (or the Euler Method).  It is also very helpful to use a spreadsheet to do the calculations.  I prove a statement from a previous projectile motion  problem video, "Air resistance decreases the x displacement of the ball by less than 1 cm."

The Excel file created in the video.

Lacrosse Ball Information:
  • Weight = 5.125 oz.
  • Drag Coefficient = 0.5
  • Circumference = 7.875 in.
  • Density of Air = 1.275 kg/m^3

Content Times:
0:22 The statement this video proves
1:01 The basic concept of air resistance
1:54 The Free Body Diagram
2:20 The Drag Force Equation
3:13 Information about the Lacrosse Ball
4:03 The Drag Coefficient
4:55 The Density of Air
5:18 How the Drag Force affects the motion
5:58 The basic idea of Numerical Modeling (or the Euler Method)
6:50 Solving for the acceleration in the x direction
8:53 Solving for the final velocity in the x direction
9:54 Solving for the final position in the x direction
11:41 Entering the Lacrosse Ball information into Excel
13:34 Solving for the Drag Force in x direction in Excel
14:29 Solving for the acceleration in the x direction in Excel
14:58 Solving for the final velocity and final position in the x direction in Excel
15:46 Solving for the acceleration in the y direction
17:21 Solving for all the variables in the y direction in Excel
19:13 Click and Drag Copy. Harnessing the Power of Excel!
19:43 Understanding the numbers in Excel
20:35 Solving for the decrease in the x displacement caused by the Drag Force