Need Help in this Numerical Methods question

**hus2020** · January 9th 2009, 07:21 PM

Hi,
Below is the questions :

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

**skeeter** · January 10th 2009, 09:11 AM

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 $k$ .

**hus2020** · January 10th 2009, 06:54 PM

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?

**Grandad** · January 10th 2009, 10:19 PM

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

**HallsofIvy** · January 11th 2009, 03:52 AM

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.

**hus2020** · January 12th 2009, 12:47 AM

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

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