And here is the code:

package pingpong2;

import java.awt.Color;
import java.awt.Graphics;
import java.awt.Point;
import java.awt.geom.*;
import java.math.*;
public class PingPong extends Game {
	public static final int BATWIDTH=60;
	public static final int BATHEIGHT=20;
	private int batX=150, batY=400;
	private int ballX=150, ballY=50;
	private int ballSpeedX=0; //the ball speed on the X axis
	private int ballSpeedY=9; //the ball speed on the Y axis
	private static final int BALLRADIUS=10;
	public void init(){
	resize(600,600);
	setSleepTime(50);

	}
	public Color getBackgroundColor(){
	return Color.black;
	}

	public void paint(Graphics g) {
	ballX=ballX+ballSpeedX;
	ballY=ballY+ballSpeedY;
	checkCollisions();
	g.setColor(Color.red); //To make the bat red
	Point mp=gp.getMousePosition(); //point mp will hold the coordinates of the mouse
	if(mp!=null)
	{
	//Then, if the mouse is in the game window, it's coordinates are copied to
	//batX and batY. If the mouse is out of the game window, batX and batY will not change.
	batX=mp.x;
	batY=mp.y;
	}
	//finaly, to draw the bat, I call the Garphics method fillRect, that draws and fills
	//a rectangle.
	g.fillRect(batX-BATWIDTH/2,batY-BATHEIGHT/2,BATWIDTH,BATHEIGHT);
	g.setColor(Color.green);
	g.fillOval(ballX-BALLRADIUS,ballY-BALLRADIUS,BALLRADIUS*2,BALLRADIUS*2);
	}
	public void checkCollisions(){
	if(ballX-BALLRADIUS<0){
	ballSpeedX=-ballSpeedX;
	}
	if(ballY-BALLRADIUS<0){
	ballSpeedY=-ballSpeedY;
	}
	if(ballX+BALLRADIUS>600){
	ballSpeedX=-ballSpeedX;
	}
	if(ballY+BALLRADIUS>600){
	ballX=150;
	ballY=50;
	ballSpeedX=0;
	ballSpeedY=9;
	}
	Ellipse2D.Double ball=new Ellipse2D.Double(ballX-BALLRADIUS,ballY-BALLRADIUS,BALLRADIUS*2,BALLRADIUS*2);
	if(ball.intersects(batX-BATWIDTH/2,batY-BATHEIGHT/2,BATWIDTH,BATHEIGHT)){
	ballSpeedX=(ballX-batX)/5;
	ballSpeedY=-(int)Math.sqrt(81-ballSpeedX^2);
	}
	
	}
}