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

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The discussion focuses on deriving the time taken for a body to reach its maximum height when thrown upward with an initial velocity u, while experiencing a resistance force proportional to its velocity. The equations of motion are established, leading to a differential equation that incorporates gravitational acceleration g and resistance coefficient k. The user attempts to solve for time by integrating the velocity equation and applying initial conditions. There is a moment of uncertainty regarding the sign conventions for gravity and resistance forces. The conclusion indicates that the user's working appears correct, but they are questioning the treatment of the forces involved.
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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?...
 
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