we can model the velocity of a falling object like a parachutist with the following differential equation:

du

di

$=3$

m

where v is velocity $($m$/$s$),1=$ time $($s$),$ g is the acceleration due to

gravity $(9\mathrm{.}81$ m$/$s~$),$ ca $=$ a second$-$order drag coefficient $($kg$/$m$).$

and m $=$ mass $($kg$).$ Solve for the velocity and distance fallen by a

$90-$kg object with a drag coefficient of $0\mathrm{.}225$ kg$/$m$.$ If the initial height is $1$ km$,$ determine when it hits the ground. Obtain your solution with $($a$)$ Euler's method and $($b$)$ the fourth$-$order RK method using hand calculation