Question

In MATLAB write a program that given the parameters from problem 13.171 (pg 900) that calculates the horizontal and vertical position of the ball after it strikes point A and until it lands at point B. Use a time increment in seconds that results in a smooth curve. Fully document your script file including a problem description and fully label your graph.

from vector mechanics for engineers eleventh edition (Beer, Johnston...) chapter 13 problem number 171

8:24 PM Vector Mechanics for Engineers Chapter 13 Problem 171P iPad 41% . v Expand all steps Step 1 Draw the schematic of the trajectory of the ball. 3 ft 60 Step 2 Step 3 0 Step 4 Step 5 Step 6 0 Step 7 0 Step 8 Step 9 Step 10 0

Answer 1

STEPS TO RUN THE CODE

-COPY THE CODE

-OPEN MATLAB AND THEN CREATE NEW SCRIPT

-PASTE THIS CODE THERE AND CHECK FOR FORMATTING ERRORS AND RUN IT

-A GRAPH WILL BE DISPLAYED SHOWING THE REQUIRED DIAGRAM

- X AND Y VALUES FOR DIFFERENT TIMES WILL BE DISPLAYED IN COMMAND WINDOW(NOT REQ FOR SOLUTION, GIVEN FOR UNDERSTANDING)

CODE

%%%%%%%%%%%%%%SECTION 1-INITIALIZATION OF VALUES%%%%%%%%%%%%%%%%%%%%%%%

syms xnew ynew
colorstring='kgbry'; %TO GIVE COLOUR
H=3; %initial height ,inft
alpha=60; %Angle OF WALL INCLINATION in DEGREES

g=32.174; %gravitational acceleration in ft/s^2
vo=25;
e=0.9;
dt=0.01;
t=0;

%SECTION2-CALCULATION OF INITIAL VELOCITIES AND POSITION OF THE PROJECTILE%

vt=vo*(sind(90-alpha));
vn=vo*e*(cosd(90-alpha));

vxo=vn*(cosd(90-alpha))-vt*(sind(90-alpha));
vyo=vn*(sind(90-alpha))+vt*(cosd(90-alpha));

x=H/tand(alpha);
X=H/tand(alpha);
y=H;
Y=H;

%%%%%%%%%%%%%%%SECTION 3-PLOTTING THE WALL AND THE FLOOR%%%%%%%%%%%%%%%

A=0;
B=0;
Anew=A+(H+2)/tand(alpha);
Bnew=B+H+2;
plot ( [A Anew] , [B Bnew],'-r','Color', colorstring(1)); hold on
xlabel('X distance');
ylabel('Y distance');
title('Path of the ball');

A=-15;
B=0;
Anew=0;
Bnew=0;
plot ( [A Anew] , [B Bnew],'-r','Color', colorstring(2)); hold on

%%%%%%%%%%%%SECTION 4-PLOTTING THE PATH OF THE BALL%%%%%%%%%%%%%%%%%

while (y>0) %calculate until trajectory goes out of
%bounds
t=t+dt; %incremcwent time
xnew=X-vxo*t; %compute new x-position
ynew=Y+vyo*t-0.5*g*(t^2); %compute new y-position

%to display values of x and y for various time(not required for the
%solution)

V=fprintf('At time t= %d x= %d y=%d',t,xnew,ynew);
disp(V)

%plot latest segment of trajectory:
plot ( [x xnew] , [y ynew],'-r','Color', colorstring(3)); hold on

x=xnew;
y=ynew; %update values of x and y
end
legend('wall','floor', 'path of the ball');
hold off

Output graph:

Path of the ball 10 wall loor -path of the ball 4 16 14 12 10 -8 -6 4. X distance