This document summarizes a numerical analysis project using the Euler method to simulate projectile motion in MATLAB. It contains sections on the Euler method, applying it to physical systems like projectile motion, implementing it theoretically and in MATLAB, and presenting the output and conclusions. The group members are listed and the document contains the equations of motion for a projectile and details on setting up and running the simulation in MATLAB.

1. Numerical Analysis
Project
Projectile Motion
Using
MATLAB

2. Group Members
Awais Ahmad
(Group Head)
12-
EE(E&T)-11
M. Ahmed Waqas
12-
EE(E&T)-031
Adeel Ahmed
12-
EE(E&T)-004
Faheem Khan
12-EE(E&T)-013
Farhan Abbas
12-EE(E&T)-016

3. Contents
• Euler Method
• Physical Aspects of this Method
• Practical Implementation
• Code and Input
• Output
• Conclusion

4. Euler Method
• The Euler method is
y{n+1} = y(n) + hf(t(n),y (n)).
so first we must compute f(t(0), y(0)). In this simple differential equation,
the function f is defined by f(t,y) = y

5. Physical Aspects of This Method
• Measuring the Period of Oscillation
• Measuring the Velocity of Projectile Motion
• Measuring the Current and Voltage of RC,RL,RLC Circuits.
• Measuring the torque of motor
… In short any 1st Order IVP can be solved

6. Practical Implementation
(Projectile Motion)
Solution
By Theoretical
Implementation
Projectile
System
By using
MATLAB

7. Theoretical Implementation
• Given that:-
• mV` =Fg + Fr ;where as Fg=-m*g , Fr=-kV|V|
• Also , g=9.8ms-2 ; k=0.002kg/m ; m=0.11kg ;V0=8ms-1
• As
• |V|={ +V -V }
• By Putting Values and Simplifying we have 1st Order Differential Equation
V`= - 9.8 - 0.1818 V2

8. Using MATLAB

9. Output

10. Graphical Representation