A lion and a lion tamer are enclosed within a circular cage. If they move at the same speed but are both restricted by the cage, can the lion catch the lion tamer? (Represent the cage by a circle, and the lion and lion tamer as two point masses within it.)
(In reply to solution
Completely right, for point masses.
Of course, the tamer point does not need to go all the way to the wall. She can stop at any radius, and circle at top speed, and the lion point will never catch her. However, it is easier to circle at a fixed radius if you have a wall to guide you, as long as wall friction and subatomic forces don't make you slower than the lion.