# A Brief Look at the Force of Drag using Numerical Modeling (or The Euler Method)

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.”

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

Click Times for Content:
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

Want lecture notes & the Excel File?
http://www.flippingphysics.com/the-euler-method.html
(also contain’s photo credits and links to website’s shown in video)

The original problem videos for this are:
(part 1 of 2) An Introductory Projectile Motion Problem with an Initial Horizontal Velocity
http://www.flippingphysics.com/projectile-motion-problem-part-1-of-2.html

(part 2 of 2) An Introductory Projectile Motion Problem with an Initial Horizontal Velocity
http://www.flippingphysics.com/projectile-motion-problem-part-2-of-2.html

How Many Attempts did it Really Take? – with live music from Amos Lee
http://www.flippingphysics.com/how-many.html

1¢/minute: http://www.flippingphysics.com/give.html