I am currently stuck on this question.
A woman is running along the line x = 50 (assuming constant speed)
Her dog returns a ball to her but runs in a curved line, as the dog runs towards wherever she is at any instant. To simplify the problem, we assume that the dog starts his journey to her from the origin of suitable rectangular axes, whilst she sets off on her run from (50,0) at the instant the dog starts his run with the ball from the origin.
I am required to formulate a discrete model and a continuous model, and an equation involving the dogs position, the gradient of its location in the x/y plane and the position of the woman, this is all in order to find the position and displacement of the dog at any given time.
Thank you, I will update my post if I make any advance.