John is thrown into the outer part of a circular den of radius a. At the centre of the den is a Lion. John decides his best tactic is to run round the perimeter of the den with his maximum speed u. The Lion responds by running towards John with its maximum speed U.
(i) Sketch the path taken by the Lion.
(ii) Show that the distance r of the Lion from the centre of the den satisfies:
dr/dt = sqrt [U^2 - r^2u^2/a^2]
(iii) Hence find r as a function of t.
(iv) Show that if U > u John will be caught by the Lion.
(v) What happens in the special case where u = U?
The Attempt at a Solution
For i) I sketched the path of the lion to be a spiral starting from the centre and tending outwards towards the circumference of the circle.
It's on ii) that I'm not sure on how to set up the problem and the relevant equations of motion that would yield the desired equation. Any hints?