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TAM 203 Homework 1 Page 3/6

9.23)

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TAM 203 Homework 1 Page 5/6

9.26)

function homework926 ( )% Problem 9.26 Solution% Jan 29, 2008

% VARIABLES (Assume consistent units)% +x = displacement% v = dx/dt% z = [x v] f z is the 'state vector1

% CONSTANTSc= 1 ; % drag constantpw= 1000; % density of water (kg/m^3)m= .002; % mass of bullet (kg)d= .0057; % diameter of bullet (m)

A- pi/4*dA2; % area of bullet (mA2)

% INTIAL CONDITIONSvO= 400; % initial velocityxO= 0; initial positionzO= [xO vO] ;

tspan =[0 1] ; %time interval of integration

error = le-4;% Set error tolerance and use 'event detection'options = odeset ( ' abstol ' , error, ' reltol ', error, ...

'events', @stopevent) ;

% Ask Matlab to SOLVE odes in function f rhs '[t zarray] = ode45 (@rhs, tspan, zO, options, c, pw,m, d) ;

The parameters m, c and g are passed to both% the 'rhs' function and the 'stopevent' function% Each row of zarray is the state z at one time.

%UNPACK the zarray (the solution) into sensible variablesx = zarray (:,1); x is the first column ofv = zarray (:, 2); is the second column ofdisp (x (end) ) ;

lot (t,x)itle(f Bullet Problem1)label ('Time, t'); ylabel (' Position, x')axis([0 inf -inf inf ] ) %inf self scales plot

end % end of main function

TAM 203 Homework 1 Page 6/6

% THE DIFFERENTIAL EQUATION f The Right Hand Side1

function zdot = rhs (t, z, c, pw,m, d)%UNPACK state vector z into sensible variablesx = z(l); y is the first element ofv = z(2); v is the second element

%Define Constant Area of BulletA= l/4*pi*dA2;

%The equationsxdot = v; % kinematic relation between x and vvdot = -l/2*c*pw*vA2*A/m; % F = m a

% Pack the rate of change of x, v into a rate of change% of state:zdot = [xdot vdot]1; % Has to be a column vectorend % end of rhs

^

function [value, isterminal, dir] = stopevent (t, z, c,pw,m, d)% Have to assign numbers to value, isterminal, dir%UNPACK z into sensible variablesx = z(l); x is the first element ofv = z(2); is the second element ofvalue = v-5; % stop integrating when v=isterminal = 1; 1 means stopdir = -1; -1 for decreasing, + 1 for increasing,

% 0 for any which way.end % end of stopevent

Output: The total penetration distance when the velocity has dropped to 5 m/s is 0.687 meters,Bullet Problem

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