Hi,
Below is the questions :
Can somebody show me the working on how to solve it. Thank you.
let $\displaystyle k = \frac{c}{m}$
$\displaystyle \frac{dv}{dt} = g - kv$
$\displaystyle \frac{dv}{g - kv} = dt$
$\displaystyle \frac{-k}{g - kv} dv = -k \, dt$
$\displaystyle \ln|g - kv| = -kt + C_1$
$\displaystyle g - kv = e^{-kt+C_1} = e^{C_1} \cdot e^{-kt}$
$\displaystyle g - kv = C_2e^{-kt}$
$\displaystyle v = \frac{1}{k}\left(g - C_2e^{-kt}\right)$
$\displaystyle v = \frac{mg}{c} \left(1 - C_3e^{-kt}\right)$
sub in your given data and determine the values of $\displaystyle C_3$ and $\displaystyle k$.
The problem is asks you to do 5 steps of a numerical integration of a differential equation. There are many different algorithms for that: Euler method, second order Runge-Kutta, fourth order Runge-Kutta, Adams-Bashforth, etc. Since none of us took the course YOU are taking, none of us know which algorithm you would be expected to use. We didn't attend the classes! Hopefully you did.