We have two cars moving like the picture. we want to find their minimum distance using relative motion.
I) Consider a coordinate system on M, which has two axis. one axis is in direction of MP and the other is perpendicular to that (Something like r_hat and θ_hat). Find the velocity of p in the new coordinate system.
II) Describe the movement of P from M viewpoint (I think it means find the equation of motion)
III) Using II, find minimum distance between the two cars?
IV) Prove that the minimum distance is zero if and only if dp/vp = dm/vm.
The picture is from Fundamentals of Physics/Resnick,Walker,Holiday but the question is different from the question of the book.
The Attempt at a Solution
I can completely solve this without the new coordinate system and using only i and j. But I have problems with this new coordinate system. I can also find something like vp→ = -vp sin θ r_hat + (-vp) cos θ θ_hat. θ is the angle between MP and Y axis. But I don't know how to find the equation of motion and solve the other parts. using the method in the question.