Thread: 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 $\displaystyle k = \frac{c}{m}$

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

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

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

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

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

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

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

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

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

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 $\displaystyle h$ represents the displacement (the height perhaps?), then $\displaystyle v =\frac{dh}{dt}$, and you'll need to integrate again to get $\displaystyle h$ in terms of $\displaystyle t$.