Learning Outcome: $\%$ Please enter your name inside the single quotes in the next line

name $=\text{'}\text{'}$; $\%$ Last Name, First Name

nameInfo $=$ isempty$($name$)$;

if $($nameInfo$==1)$

disp$(\text{'}$Please enter your name in Line $2.\text{'})$;

end;

$\%$ Define unknowns and integration variables as symbolic variables

syms c s v; $\%$ Unknowns

syms ; $\%$ integration variables

nbrSymvar $=$ length$($whos$)$;

$\%$ Given

a $=$ C$*$S;

v$0=0$;

s$0=1\mathrm{.}5$; $\%[$m$]$

s$1=3$; $\%[$m$]$

v$1=200$;

$\%$ Solve

eqn $=$ v $*$ diff$($v$,$ s$)==$ a; $\%$ Define the equation

v$\_$sol $=$ dsolve$($eqn$,$ v$($s$0)==$ v$0)$; $\%$ Solve the equation

$\%$ Display

disp$(\text{'}$You should get: The value of constant c is $28853\mathrm{.}90$ m$2.\text{'})$;

fprintf$(\text{'}$The value of constant c is $\%\mathrm{.}2$f m$2.\backslash$mp@subsup$\{$n$\}\{\}\{\backslash$prime$\},$c$)$; $\%$ Keep the two digit places

fprintf$(\text{'}$

$\text{'})$;

disp$(\text{'}$You should get: The value of constant c is $2\mathrm{.}89$e$+04$ m$2.\text{'})$;

fprintf$(\text{'}$The value of constant c is $\%\mathrm{.}3$g m$2.\backslash$mp@subsup$\{$n$\}\{\}\{\backslash$prime$\},$c$)$; $\%$ Keep three significant digits

disp$(\text{'}$Did you notice the difference between $\%$f and $\%$g$?\text{'})$;

Be able to define symbolic variables;

Be able to represent equations; and

Be able to solve for unknowns.

This assignment is to use MATLAB Symbolic Math Toolbox to find the numerical answer of a straight$-$line motion using

the chain rule.

If you have trouble completing this assignment, you may check out previous MATLAB assignments as a reference.

Problem Statement: Gas guns are used to investigate the properties of materials subjected to high velocity impacts. A

projectile is accelerated through the barrel of the gun by gas at high pressure. Assume that the acceleration of the

projectile in $\frac{m}{s^2}$ is given by $a=\frac{c}{s},$ where $s$ is the position of the projectile in the barrel in meters and $c$ is a constant

that depends on the initial gas pressure behind the projectile. The projectile starts from rest at $s=1\mathrm{.}5m$ and

accelerates until it reaches the end of the barrle at $s=3m.$ Determine the value of the constant $c$ necessary for the

projectile to leave the barrel with a velocity of $200\frac{m}{s}.$

Given: $a(s)=\frac{c}{s}\frac{m}{s^2},v_0=0,s_0=1\mathrm{.}5m,s_1=3m,v_1=200\frac{m}{s}$

Find: $c\frac{m^2}{s^2}$

$\%$ Please enter your name inside the single quotes in the next line

name $=\text{'}\text{'}$; $\%$ Last Name, First Name

nameInfo $=$ isempty$($name$)$;

if $($nameInfo$==1)$

disp$(\text{'}$Please enter your name in Line $2.\text{'})$;

end;

$\%$ Define unknowns and integration variables as symbolic variables

syms c s v; $\%$ Unknowns

syms ; $\%$ integration variables

nbrSymvar $=$ length$($whos$)$;

$\%$ Given

a $=$ c$*$s; $\%[$m$/$s$^2]$

v$0=0$;

s$0=1\mathrm{.}5$; $\%[$m$]$

s$1=3$; $\%[$m$]$

v$1=200$; $\%[$m$/$s$]$

$\%$ Solve

eqn $=$ v $*$ diff$($v$,$ s$)==$ a; $\%$ Define the equation

v$\_$sol $=$ dsolve$($eqn$,$ v$($s$0)==$ v$0)$; $\%$ Solve the equation

$\%$ Display

disp$(\text{'}$You should get: The value of constant c is $28853\mathrm{.}90$ m$^2/$s$^2.\text{'})$;

fprintf$(\text{'}$The value of constant c is $\%\mathrm{.}2$f m$^2/$s$^2.$

$\text{'},$c$)$; $\%$ Keep the two digit places

fprintf$(\text{'}$

$\text{'})$;

disp$(\text{'}$You should get: The value of constant c is $2\mathrm{.}89$e$+04$ m$^2/$s$^2.\text{'})$;

fprintf$(\text{'}$The value of constant c is $\%\mathrm{.}3$g m$^2/$s$^2.$

$\text{'},$c$)$; $\%$ Keep three significant digits

disp$(\text{'}$Did you notice the difference between $\%$f and $\%$g$?\text{'})$;