A particle of mass m is thrown vertically up with velocity u. Air exerts an opposing force of a constant magnitude F. The particle returns back to the point of projection with velocity v after attaining maximum height h, then

A

$$h = \frac{u^2}{2\left(g + \frac{F}{m}\right)}$$

B

$$h = \frac{v^2}{2\left(g - \frac{F}{m}\right)}$$

C

$$v = u\sqrt{\frac{g - \frac{F}{m}}{g + \frac{F}{m}}}$$

D

$$v = u\sqrt{\frac{g + \frac{F}{m}}{g - \frac{F}{m}}}$$