For this assignment, submit three python files named q1.py, q2.py, and q3.py along with any resources (images, sounds, etc) needed by these files.

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.
2. 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.
3. Extend your game from question 2 in the following ways:
   1. The player gets three lives. The number of remaining lives is displayed somewhere on the screen.
   2. The game has a soundtrack that plays continuously (use a short loop, not a big audio file.)
   3. The player has a score that increases by 100 for every second that their cat avoids the dog. The score is also displayed somewhere on the screen.
   4. When the dog catches the cat, some kind of depressing sound is played and the game doesn't restart until the sound is done playing.
   5. When the player loses their third life, a different depressing sound is played and a big Game Over appears on the screen. If the player clicks the mouse, the whole game resets.
   6. After every thirty seconds without losing a life, another dog appears somewhere not too close to the cat and starts chasing the cat.