Chapra Problem $1\mathrm{.}7.$ For the second$-$order drag model $($Eq$.1\mathrm{.}8),$ compute the velocity of a free$-$falling parachutist using Euler$$s method for the case where m$=80$ kg and c$\_$d$=0\mathrm{.}25$ kg$/$m$.$ Perform the calculation from t$=0$ to $20$ sec with a step size of $1$ sec$.$ Use an initial condition that the parachutist has an upward velocity of $20$ m$/$s at t$=0.$ At t $=10$ s$,$ assume that the chute is instantaneously deployed so that the drag coefficient jumps to $1\mathrm{.}5$ kg$/$m$.$

function v $=$ Chapra$\_$Problem$\_1$p$7($x$,$p$,$g$)$

$\%$ Usage: v $=$ Chapra$\_$Problem$\_1$p$7($x$,$p$,$g$)$

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$\%$ Compute velocity of falling mass using Euler's method.

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$\%\%$ Input

$\%$ x: independent variables, vector of time values and initial velocity Size: $5$ X $1$

$\%[$dt; t$0$; t$1$; tf; v$0]$

$\%$ p: parameters, vector $[$m; c$\_$d$0$; c$\_$d$1]$ Size: $3$ X $1$

$\%$ g: gravitational constant for right$-$hand$-$side gravity force $($scalar$)$ Size: $1$ X $1$

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$\%\%$ Output

$\%$ v: velocity vector $($downward speeds at each time$)$ Size: $1$ X Number of time steps between t$0$ and tf

$\%\%$ Parse input variables

dt $=$ x$(1)$; $\%$ time increment, delta$-$t

t$0=$ x$(2)$; $\%$ initial time

t$1=$ x$(3)$; $\%$ time when parachute deploys

tf $=$ x$(4)$; $\%$ final time

v$0=$ x$(5)$; $\%$ initial velocity at time t$=$t$0$

m $=$ p$(1)$; $\%$ jumper's mass

c$\_$d$0=$ p$(2)$; $\%$ drag coefficient for jumper alone

c$\_$d$1=$ p$(3)$; $\%$ drag coefficient for jumper with parachute