Develop a graphical program that simulates two billiard balls colliding on a pool table. You might want to include the effects of friction and subsequent interactions with the sides of the walls. Develop a program to determine the solution to a maze. Define a relatively simple maze and demonstrate the search for the solution. Find the most cost effective way for a person to travel to a number of cities (8 or more), given that the person wants to visit each city only once and, at the end, return to the city of origin. You should specify how you define "cost effective", e.g. shortest total distance travelled. Make an animation of a multibody system, e.g. three or more gravitating planets which are not only attracted by the sun but also by each other Direct a photon onto a lens and have it refract at each surface. This would serve as a demonstration (or simulation) of the bending of light in an optical system. Or choose to direct the photon onto one or more curved mirrors. Use Snell's Law Direct a photon of a fixed wavelength onto a prism and have it refract at each surface by an amount which depends on its wavelength in a reasonable way. Direct a non-relativistic charged particle towards a fixed charged particle and plot the path Create Lissajous figures for one or more chaotic systems. Plot the path followed by one member of a coupled double pendulum. Plot the height versus time of a rocket blasting off from the surface of the earth. A major fraction of the initial mass of the rocket is its fuel. It runs out of fuel a short time after blastoff. . Implement a Monte Carlo program (ie, using random numbers) to calculate to some high degree of accuracy 22 Y