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**puddy** example a stone is dropped from a bridge against quadratic air resistance and im deriving an expression of the stones velocity in terms of its position.

mv dv/dx=mg-mg-kv^2

integral v/g-kv^2=integral 1 dx k=6.2x10^-3

-1/2kln(g-kv^2)=x+A

g-kv^2=e^(-2kx-2kA)=Be^-2kx

g-kv^2=ge^-2kx

v=sqroot g/k sqroot 1-e^-2kx (distance stone falls is 77m)

plugging every thing in

v=sqroot 9.81/6.2x10^-3 sqroot 1-e^-2x6.2x10^-3x77=31.2 ms

now how do i solve a similar problem, a ball is projected vertically upwards with a speed of 20ms and it reaches a max height of 17.37m and i need to find in the method i have shown the time it took to reach its max height and k=0.009

if some one can show me how its done thanks ,but i want to solve it in the same kind of method ive shown no partial fractions,i have actually been told its not that hard to solve in that way.any help thanks