Here is what Wolfram Mathematica can solve:

[1]  m*a==-m*g-k*v[t]
[2]  %1/.a->v'[t]
[3]  DSolve[{%2, v[0]==V0}, {v[t]}, {t}]
[4]  Simplify[%3/.k->n*m]
[5]  (v[t]/.%4)[[1]]
[6]  Integrate[%5, {t, 0, t}]
[7]  (%6/.{V0->Vx, g->0})==s
[8]  (%6/.{V0->Vy})==0
[9]  Reduce[{%7, %8}, {s, t}]
[10] Simplify[%9 && g!=0 && n!=0 && Vx!=0 && Vy!=0]/.C[1]->0

In Out[10] there is an equation for s with Lambert function W. Can I get to 
that equation in FriCAS?

I don't have Wolfram Mathematica. I tried to reproduce steps from this video 
<https://www.youtube.com/watch?v=pFkPD7FoR3U>.

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