Solving the Projectile Motion Problem With Air Drag

AI Thread Summary
The discussion centers on solving a projectile motion problem that incorporates air drag, specifically where the drag force is proportional to the square of the speed. The key equation to derive is h = 1/2k*ln[1+(kv0^2/g)], which describes the maximum height reached by the projectile. Participants express confusion about forming the necessary differential equation and seek guidance on the initial steps. The mention of terms like "c1v" indicates a need for clarification on the forces acting on the projectile, including gravity and drag. Overall, the thread highlights the challenges of applying differential equations in mechanics without prior coursework.
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Homework Statement


A projectile with mass m is fired upward with an initial speed v0. If the air drag varies with the square of speed F(v)=-kmv2 show that the projectile reaches a height of
h=1/2k*ln[1+(kv0^2/g)]



Homework Equations


F0+F(v) = mv(dv/dx)


The Attempt at a Solution


I am a little confused on how to get started and tackle this problem! Any pointers? Thanks for the help!
 
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Were you able to get the differential equation?
 
I was not able to get the diff. eq. I have not had any diff. eq. classes yet, so I am teaching myself as I go along in my mechanics course. Would it be ma=-mg-c1v?
 
What is "c1v"?
 
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