1. Because it is circular motion, it is more appropriate to establish a polar coordinate system;

2. Assuming that the jogger moves at a uniform speed (linear speed), the dog's movement can be decomposed into uniform movement along the radial direction and circular movement with the same angular speed as the jogger.

3. The equation is established with time t as the parameter, and the angular velocity equation is extracted from the jogger's linear velocity as the angular velocity of the dog's circular motion, thus establishing the dog's radial motion equation and circular motion equation, and the simplified equation is the dog's motion trajectory equation.

4. The intersection of the two curves is the point where the dog catches up with the jogger, and the time t can be obtained by solving the equation.