Question

MATLAB model with drag force My Solutions > Background: You will be using a MATLAB model with air resistance included to predict the path of the ping pong ball. Since the drag force due to the air always opposes the motion of the ball, the system can not be modeled in a "closed form" way. In a closed form solution you can just write an equation and solve it. Instead this has to be done in an iterative fashion. Your Task: Copy the code into Matlab to open and review it. Here are the parts: Initialize Variables - Use the comments to figure out what these are. Student developed code - A section for you to imput code that uses a while loop to calculate the motion of the ping pong ball. The spaces that need code are called out with %********** ** and a hint inside about what is missing. Note the variable names suggested in these hints so that the rest of the code will work once those things are added. Plotting of final values - This plot should look like the following. distance traveled by ping pong ball in meters vertical distance traveled (meters)
CODE GIVEN

% Create a program to plot the motion of the ping pong ball with drag.

% The program will take inputs for velocity in m/s and angle of launch.

% note that with a high speed camera I estmated a launch speed for a ping

% pong ball could be 30 m/s.

vel=30; %m/s

angle=60;

% convert the degrees into radians so MATLAB likes it

angle=angle*pi/180;

% set initial values (time, distance, mass, gravity, drag)

x(1)=0; % meters

y(1)=.01; % meters

time(1)=0; % seconds

mass=.00247; %kg ping pong ball .00247 Kg

g=-9.8; % m/sec^2

c=-0.0005; % coefficient of drag with density and area in this constant

index=1; % so I can load an array for plotting

% start to increment the motion and define it component forces

velx=vel*cos(angle);

VelocityX(1)=velx;

vely=vel*sin(angle);

VelocityY(1)=vely;

% set a time step and variable for height

deltaTime=.001; % seconds

height=y(1);

while height>=0 % check that the ball has not hit ground yet

index=index+1; % setup and index

% *******************************************************

% break velocity into its components

% *******************************************************

% *******************************************************

% use an if/else statement to check to see if the ball is moving

% down (negative). If it is, then drag has an opposite sign

% as gravity in the acceleration formula. Otherwise gravity

% and drag have the same sign. Calculate the new acceleration in the y.

% *******************************************************

% *******************************************************

% Now calculate the acceleration in the x .

% *******************************************************

% *****************************************************

% calculate the new velocity at the end of the time step

% this will have X and Y components, so you need a variable

% for each. One is velFinalX and the other is velFinalY.

% *******************************************************

% ******************************************************

% Get a new velocity vector and angle given the X and Y

% The velocity is the variable "vel" and angle is "angle"

%*******************************************************

% now save my values at this time step

time(index)=time(index-1)+deltaTime;

VelocityX(index)=velFinalX;

VelocityY(index)=velFinalY;

% and distance numbers

distX=velx*deltaTime;

distY=vely*deltaTime;

% save distance values

x(index)=x(index-1)+distX;

y(index)=y(index-1)+distY;

height=y(index);

end

plot(x,y)

title('distance traveled by ping pong ball in meters')

xlabel('horixontal distance traveled (meters)')

ylabel('vertical distance traveled (meters)')

Answer 1

Solution:---

clc
clear all
close all
format long
x=0;
y=0;
t=0;
i=1;
v0=100;
th=pi/4;
cd=0.6;
g=9.81;
while(y(i)>=0)
t=t+0.001;
x(i+1)=v0*cos(th)*t-0.5*cd*t^2;
y(i+1)=v0*sin(th)*t-0.5*cd*t^2-0.5*g*t^2;
i=i+1;
end
y=y(1:end-1);
x=x(1:end-1);
plot(x,y);
xlabel('horizontal distance travelled');
ylabel('vertical distance travelled');

- 5 x Pradeep - 0 X 56 Search Documentation Tax x eulerSystem.m Xahk. mx nse_filt.m x + 1 A MATLAB R2018 HOME PLOTS APPS EDITOR Figure 1 E D L Find Files Insert B fx File Edit View Insert Tools Desktop Window Help 3 Compare - -Go To - Comment % 99 O A BO E New Open Save Print F ind Indent 1 1 FILE NAVIGATE EDIT 250 - hal Windows System32 Current Folder Name 200 0409 1029 1033 1036 1040 1045 1046 1049 1055 3082 Advancedinstallers af-ZA am-et AppLocker appraiser Details O 100 200 300 400 500 600 700 Workspace horizontal distance travelled Name Value cd 0.6000 g 9.8100 13587 13.5860 th 0.7854 vo 100 1x13586 double 1x13586 double vertical distance travelled 800 900 1000 x By script Ln 23 Col 39 ENG 12:56 PM US 02/26/20 Type here to search

Thanks.