A small stone of mass `m` is thrown vertically upwards with an initially speed `v`. If the air resistance at speed `v` is `m k v^(2)`, where `k` is a constant, show that the strone returns to the starting point with a speed `v (1 + (kv^(2))/(g))^(-1//2)`

Explanation

`F_(R) = - mkv^(2)`
`F_(g) = - mg`
`m xx a = - m [kv^(2) + g]`
`(vdv)/(ds) = - [kv^(2) + g]`