Math Help - Need Help in this Numerical Methods question

1. Need Help in this Numerical Methods question

Hi,
Below is the questions :

Can somebody show me the working on how to solve it. Thank you.

2. let $k = \frac{c}{m}$

$\frac{dv}{dt} = g - kv$

$\frac{dv}{g - kv} = dt$

$\frac{-k}{g - kv} dv = -k \, dt$

$\ln|g - kv| = -kt + C_1$

$g - kv = e^{-kt+C_1} = e^{C_1} \cdot e^{-kt}$

$g - kv = C_2e^{-kt}$

$v = \frac{1}{k}\left(g - C_2e^{-kt}\right)$

$v = \frac{mg}{c} \left(1 - C_3e^{-kt}\right)$

sub in your given data and determine the values of $C_3$ and $k$.

3. thx for the simplified equation. But, still I am unclear of where do I replace the 'h' value that is given & the question is asking me the 'time' right, not velocity?

4. Differential equation

Hello hus2020
Originally Posted by hus2020
thx for the simplified equation. But, still I am unclear of where do I replace the 'h' value that is given & the question is asking me the 'time' right, not velocity?
If $h$ represents the displacement (the height perhaps?), then $v =\frac{dh}{dt}$, and you'll need to integrate again to get $h$ in terms of $t$.

Grandad

5. 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.

6. yes, the question requires to use the Euler's method since the others are not taught yet.