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I have no problems regarding relative velocity in one-dimension, thats quite simple. But this relative velocity concept in two-dimensions is really really confusing specially when it comes to solving problems. Believe me or not, i have been trying to understand this concept for the past almost one year or so. But its impossible. I have never faced such a problem in my life, and i guess i wont face it in future either. I'm so agitated that i now go around saying that even if i become one of the greatest physicists in the world, even then i will not be able to do problems from one chapter- and that is relative velocity. I understand all other concepts and dont have much trouble solving problems from other chapters myself(and ofcourse with PF help at times, thanks for that). But i am not even able to solve the simplest problems of this "relative velocity".

I'll explain my problem in detail. See, i do understand the theoretic part, somewhat. But whenever i sit down to do problems, i have varied difficulties and am unable to solve them. I have gone thru many books and solved exaples but still dont get it. each problem seems to pose more problems and they seem to be done differently from each other. I have so many ... anyway here i'll just post a few:

"Rain is falling vertically with speed 4m/s and the man is moving due east with a speed 3m/s. with what speed the rain appears to be coming to man and where should he hold the umbrella to protect himself from rains?"

QUESTIONS THAT TROUBLE MY MIND: (1) what should be the vector relation or equation? (2) Is it v(man wrt ground) + v(rain wrt ground) = v(rain wrt man) ? (all r vectors ofcourse).

Again there is this weird swimmer problem, shortest path, shortest time, all that crap. I cant even form the equation. If only i can form the equation, then only will i resolve the vectors along chosen axes and then find the answer. but i cant form the vector relation. whose velocity with respect to whom plus whose velocity wrt whom will i add? Its all too confusing, even i cant explain my problem. This is the worst topic in physics. No other concept in the world is as confusing as "relative velocity". I feel suicidal. Please please help me, i beg u.

Once again sorry for not presenting my thread well, as always. But i promise that i'll be back with my well organised threads as soon as i understand this concept. If PF cant explain it, then no one on earth can. Thanks a lot.