Find Time to Reach Max Height for Kinematic Q w/ g,k,u Variables

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Homework Statement


A body of mass m is thrown upward with intial velocity u, in a medium which exerts a resistance force of mkv. Express, in term of g, k and u, the time taken for the body to reach its maximum height


Homework Equations





The Attempt at a Solution



a = -g - kv
dv/dt = -g - kv
-dv/(g+kv) = dt
t = -1/k ln|g+kv| +c
when t = 0, v=u
c = 1/k ln|g+ku|
t = -1/k ln|g+kv| + 1/k ln|g+ku|
At maximum height, v = 0
Thus t = -1/k ln|g| + 1/k ln|g+ku|
Is my working correct?
 
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looking quickly i think so... can't see any problems
 
wait... if taking gravity as negative the resistive force would be + first equation?...