gibson:teaching:fall-2013:math445:lab11
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gibson:teaching:fall-2013:math445:lab11 [2013/12/05 07:16] gibson |
gibson:teaching:fall-2013:math445:lab11 [2013/12/05 09:10] (current) szeto |
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| %%(c)%% If $\theta = \pi/4$, how much do you have to increase the initial velocity so the x distance is as large as it is without air resistance? | %%(c)%% If $\theta = \pi/4$, how much do you have to increase the initial velocity so the x distance is as large as it is without air resistance? | ||
| - | Hints: It's probably easiest to answer (a)-%%(c)%% if you turn your script into a function ''xdistance = projectile(v0, theta)'' that returns the distance the projectile travels as a function of the initial velocity and angle. You can compute ''xdistance'' accurately from an ''x,y'' trajectory using interpolation: | + | Hints: It's probably easiest to answer (a)-%%(c)%% if you turn your script into a function ''xdistance = projectile(v0, theta)'' that returns the distance the projectile travels as a function of the initial velocity and angle. |
| + | In other words, create a new function "projectile.m" | ||
| + | <code> | ||
| + | function xdistance = projectile(v0,theta) | ||
| - | xdistance = interpolate(x(2:end,2), x(2:end,1), 0); | + | rho_air = 1.28; % kg/m^3, density of air |
| - | + | rho_iron = 7870; % kg/m^3, density of iron 7.87 gm/cm^3 == 0.00787 kg/(0.01m)^3 = 7870 kg/m^3 | |
| - | That will return the value of $x$ for which $y=0$, i.e. where the cannonball hits the ground. Once your function works, play around with the parameters ''v0, theta'' to answer the questions. | + | C_D = 1; % drag coefficient for sphere |
| + | g = 9.81; % m/s^2, acceleration due to gravity | ||
| + | . | ||
| + | . | ||
| + | . | ||
| + | f = @(t,x) [ ....]; | ||
| + | |||
| + | [t,x]= ode45(f,[0:0.1:200] ,[ 0,0,v0*cos(theta), v0*sin(theta) ); | ||
| + | |||
| + | xdistance = interp1(x(50:end,2), x(50:end,1), 0); % This is how you can compute ''xdistance'' | ||
| + | % accurately from an ''x,y'' trajectory using interpolation. | ||
| + | % It will return the value of $x$ for which $y=0$, i.e. | ||
| + | % where the cannonball hits the ground. | ||
| + | |||
| + | end | ||
| + | </code> | ||
| + | |||
| + | Once your function works, play around with the parameters ''v0, theta'' to answer the questions. | ||
| + | On the command line, you can USE this function like this. | ||
| + | <code> | ||
| + | xdistance = projectile(100,pi/2) | ||
| + | xdistance = projectile(100,pi/4) | ||
| + | xdistance = projectile(100,pi/8) | ||
| + | </code> | ||
| + | |||
| + | |||
| + | If your xdistance is a NaN, you may have to increase the number 50 in the interp1 function (1000 might be good, that is roughly half the length of [0:0.1:200]). | ||
| | | ||
gibson/teaching/fall-2013/math445/lab11.1386256600.txt.gz · Last modified: 2013/12/05 07:16 by gibson
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