3. A dog, a cat, and a mouse, are located at the corners of an equilateral triangle with respective locations (\"5/2, 1/2), (0,1), and (/2, 1/2) meters, shown to the right. At time 0, the dog starts chasing the cat, the cat chases the mouse, and the mouse chases the dog, as shown by the red / arrows. Each moves a. the same constant speed of 1 meter ' . H l ' dog (*9 -%) - cat 0(0, 1) - 1 m/s per second that they maintain for as long as they run. As mouse . , .\" all three animals keep moving, their directions will change (_ E. _ %) with time, at some point following the blue arrows, etc. T (a) Find the speed at which the dog approaches the cat, namely the rate at which the distance between them decreases, at time 0*. (b) Argue that the speed in part (a) remains the same throughout the chase, and nd how long it will take the dog to reach the cat. (0) Find the speed at which the dog approaches the origin (0, 0) at any given time. Hint: you can optionally use this result to verify your answer to part (b). C" 4 ((1) Draw a rough, or even very rough, sketch of the trajectories of the three animals