mv dv/dx= -mg-kv^2. See the difference? Understand why? Now integrate etc.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.
integral v/g-kv^2=integral 1 dx k=6.2x10^-3
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