Lab 8 - Bounce

You may have a partner for this lab.

Introduction:

Your task is to implement and animate a user controlled simulation of a ball falling under the influence of gravity in a box and bouncing until it stops. Let the user start and stop the simulation by pressing a button. Make the radius of the ball 20 pixels and its color red. Assume the elasticity of the collision with the floor is 90%; thus if the downward velocity of the ball were 100 when it hit the floor, its subsequent upward velocity would be 90.

A dropped ball bouncing straight up and down under the effect of gravity will need two state variables; one for its height from the floor and one for its velocity (up or down). Given a position and velocity and a gravitational constant, its position and velocity at the next time step can be computed using equations from elementary physics. Using standard physics notation; s stands for position, v for velocity, and a for acceleration. As you might guess v_t is the velocity at time t, v_t+1 is the velocity at the next time step. Thus the transition function may be written as two equations:
s_t+1 = s_t + v_t
v_t+1 = v_t + a_t
So the ball's height at the next time step is just its current height plus its current velocity; its velocity at the next time step is just its current velocity plus the acceleration due to gravity.

If you have not studied physics, those equations may seem a bit mysterious; but they are quite simple once you understand them. If a ball is travelling at 10 pixels/step and is currently at location 100, after the next step it will be at 110. In symbols, s_t = 100, v_t = 10, s_t+1 = s_t + v_t = 100+10 = 110. Velocity is updated similarly.

Extra credit!

1) Modify your code so that the Ball can be thrown to start the simulation. All that is needed is an additional initializing constructor that takes two additional parameters, the x-velocity and y-velocity.

    public Ball(int x, int y, int r, Color c, int vx, int vy) { 
        this(x,y,r,c); 
        this.vx = vx; 
        this.vy = vy; 
    }

Then you can initialize the ball with:

        theBall = new Ball(10,100,20,Color.RED, 2, -20);

For this to work, you must also update the x-coordinate in Ball:step()

2) Add code to keep the Ball in the box. ItÕs just like the bounce code except you must check for hitting the other sides of the box.

3) Add another Ball (or two) going in a different initial direction. Add 5! Hint: ArrayList<Ball>

4) Make them interact. Make them bounce instead of passing through each other. Or, make them repulsive (er, to each other).

4) Make the walls perfectly elastic (so the Balls don't slow down when they bounce. Turn off the gravity. Fun, fun, fun!

Lab 8 - Bounce

Introduction:

Extra credit!

How to get credit: demo in lab on Thurs!