Let's write our first numerical method to solve this same problem! Create a new function called forward$\_$Euler$\_$velocity$().$ This function will take in the same exact inputs and provides the same form of output as in the exact$\_$velocity$()$ of Problem $1.$ However, instead of computing the exact solution to the model we will approximate the time derivative using the forward

Euler approximation:

delv$\frac{t}{d}$elt~~$v(t+t)-v\frac{t}{}t$

so that we have the following algebraic problem to solve at a given time step:

$v(t+t)-v\frac{t}{}t=g-(c\frac{d}{m}{)}^{***}v(t{)}^{{?}^{{?}^{?}}}2$

Hint: For this problem we are assuming the input $t$ will always include our initial time of $t=0.$ The code should roughly be structured as follows:

$cd,m,t,$glarr user input

ntlarr length $(t)$

vlarr an array same length as $t$

$v(0)larr0$

ilarr$1$

while $i$ nt do

$tlarrt(i)-t(i-1)$

$v(i)larrv(i-1)+t(g-c\frac{d}{m^{***}}v(i-1{)}^{{?}^{{?}^{?}}}2)$

ilarri$+1$

end while. please code in python