A cat sitting in a field suddenly sees a standing dog. To save its life, the cat runs away in a straight line with speed u. Without any delay, the dog starts with running with constant speed v>u to catch the cat. Initially, v is perpendicular to u and L is the initial seperation between the two. If the dog always changes its direction so that it is always heading directly at the cat, find the time the dog takes to catch the cat in terms of v, u and L.
As of the time of posting this. I'm not sure if there's a simple elegant solution to this, but the history of olympiads questions tells me it's probably a really complicated solution.
It's probably more logic and calculus than any kinematics equation.
The Attempt at a Solution
So far i've gotten to resolving U as a vector into it's horizontal and vertical component. Taking the instantaneous direction of V as the horizontal. Taking the angle between U and the horizontal as A.
This yields the velocity of the dog, relative to the cat as V - UcosA
I'm thinking of graphing V-UcosA with time. Not really sure how to proceed from here. '