Bouncing Ball

HEY EVERYBODY!

I'm trying to make a soccer 2D game for someone and there's a problem with the physics i'm trying to implement. (Too bad we don't learnt how to implement physics equations into code at school!) I wan't to make a ball that bounces like a normal ball in real life. So with friction, and gravity so that it doesn't keep bouncing for ever! I also want to make it so that when one of the players applies a force onto it, I want it to fly like a ball does when you head it! Any ideas? What equations must I use and how must I implement them? THANK YOU!

Here is all you need:

Acceleration of gravity: 9.8 m/s/s

All you need:
(m = metres, s = seconds, kg = kilogrammes (weight))
Distance - m
Speed - m/s
Acceleration - m/s/s
Time - s
Newtons (Force) m/s/s*kg
Friction = F (force that the object is being applied to the surface by (usually 9.8(gravity)*kg)) * X (amount of friction from the surface)
F*X, easy enough right? So if you have a 2 kg ball that starts 5m above the playing field, going 5m/s (no accel on horizontal) how fast will it be going after the first bounce?
X = on x axis, I = initial, F = final

D = 5
S(x) = 5
S(yi) = 0
S(Yf) = ? : -9.9
A(x) = 0
A(y) = -9.8
T = ? :: 1.01
F(yi) = -9.8 * 2 = -19.6
F(yf) = ?
Fric = -9.8 * 2 = -19.6


A few equations...
S(f)^2 = S(i)^2 + 2*A*D so to find the final Y speed:
X^2 = 0^2 + 2*-9.8*5=-98
sqr(x^2) = sqr(-98) = -9.9 (that'll give an error, do Sqr(98)*-1)


Now since speed is m/s and distance is m, you can isolate S for the time (you want the AVERAGE speed):
T = D / [ (S(i) + S(f) ) / 2 ]
X = 5 / [(0 + -9.9)/2] = -1.01 (obviously this won't be negative, so change it to 1.01)
Note that you don't really need the time here :p

So, the final speed is when the ball HITS the ground. Now assuming this ball defies a few laws... such as staying on the ground for more then .00000000000000001 seconds...

Answer = S(f) - 19.8
Now remember that friction can't let you put the speed below 0, so the answer is 0.

Note that: In most games gravity isn't as high as 9.8 and grass won't have a friction of 2.



That concludes your 5 minute physics class. Ask away.

Really basic physics, but a nice way of putting it - thanks!