(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A body of mass is projected with speed and moves under uniform gravity in a medium that exerts a resistance force of magnitude (i) mk*abs(v) or (ii) mK*(abs(v))^2 , where k and K are the positive constants and v is the velocity of the body. Gravity can be ignored. Determine the subsequent motion in each case . Verify motion the motion is bounded in case i , but not in case ii

2. Relevant equations

F=D+L

3. The attempt at a solution

for case i m*dv/dt= m*k*abs(v)

applying seperation of variables, I get

dv/abs(v)=kdt ==> ln(abs(v))=kt ===> v=Ce^-kt or v=Ce^kt , C being a constant and v depending on whether or not is positive or negative.

for case two, my physical system is the quadratic resistance

dv/dt=mk*(abs(v))^2

applying once again the seperation of variables method I get:

-1/K*1/v=t ==> v=-1/kt+C

I don't understand how to verify that the body is bounded. I know that a body is bounded if it cannot overcome its gravitional potential energy. I don't understand how I can possibly ignore gravity , unless the body is completely immersed in a vacuum and that cannot be possible if a fluid force is exerting a force on the object.

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# Homework Help: Resisted Motion

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