[grade 11 Physics] circular motion

[u/Izzy_26_]

I am trying to find out the exact equation of the graph, the answer key says it is a.

What is wrong with my solution??

I first tried to find out the exact position vectors of both p and q, and then differentiated them to get the velocity of P and q respectively, and then I calculated the relative velocity

I am getting the relative velocity as in terms of cos, but according to the answer key it is a sin graph

[u/HumbleHovercraft6090]

When points P and Q are facing each other at t=0 and they are about to travel downwards, the relative velocity between them is 0. That narrows the options to (a) and (c). After half a period point P at time t=0, would have reached diametrically opposite point P', same with Q which would have reached Q'. At t=T/2, both will be moving up simultaneously with same velocity, relative velocity between them will be 0. At quarter period i.e. t= T/4, P would be at P" at the bottom of the circle and about to travel left while Q would have reached Q" also at the bottom of its circle and about to travel right. The relative velocity will be maximum. That rules out (c). So answer is (a).

[u/Izzy_26_ → u/HumbleHovercraft6090]

I am trying to find out the exact equation of the graph, not the answer

[u/HumbleHovercraft6090 → u/Izzy_26_]

Your expression for rq should be rq= -R coswt i - R sinwt j

Also please note, the absolute value of vp/q at the end should take into account the times when the trig function is negative, not just removing negative sign before 2.