Need help - projectile motion with air resistance

[don_anon25]

Need urgent help -- projectile motion with air resistance

Consider a projectile fired vertically in a constant gravitational field. For the same inital velocities, compare the times required for the projectile to reach its maximum height (a) for zero resisting force and (b) for a resisting force proportional to the instantaneous velocity of the projectile.

For a, I get t=-v0/a.
For b, I have the equation F= m dv/dt=kmv-mg, which leads me to
dv/dt=kv-g.
Is this correct...If so, I can take it from here.
If not what should it be?? What should my initial condition be to solve for the constant? Should it be v(t=0)=v0?

Thanks much!

 

[Fermat]

The resisting force is simply kv, rather than mkv and it is acting in the same direction as the gravitational force, mg.

Initial/end conditions are v_i = v_o and v_f = 0.