The question:

A sphere of mass M(kgs), is fired upward with an initial velocity of 10m/s.

It's motion obeys the law dv/dt= -g-(b/a)*v*|v| where v(t)=initial velocity at time t

where g=10m/s^2 and b/a=1/10 m^-1

(a)Find the time t1 at which it reaches its maximum height where v(t1)=0

so t1= ?

(b)Find an expression for v(t) for t>=t1

so v(t)= ?

so for question (a) the teacher gave an example and ended up with a really long equation that i have no idea where it came from, V(t)=sqrt(ag/b)*tan(k-sqrt(bg/a)t) using this formula i get pi/4

I need help finding where the quation of V(t) came from please.