Using pygame implementations in python, create the following applications/games

1. Implement a simple application in which an image of your choice chases after the mouse cursor. Initially the image starts moving in the direction (0,0). During each frame, the object looks at the current location of the cursor using pygame.mouse.get_pos() and updates it's direction to be direction = .9*direction + v where v is a vector of length 10 that points from the center of your image to the mouse position.

Implement a simple game of "Dog and cat" in which the player controls a "cat" (or ball or something) that follows the mouse cursor using the same rules as question 1. The "dog" then follows the "cat" using the same rules, except that the dog's vector, v, is only of length 8. The game is over when the dog catches the cat.