I've found a new way to entertain myself!.. There's a game in my ipod, u know the one where you control a bar and keep hitting a ball upwards to destroy coloured blocks??.. haha, I'm now at a super high level..

Okie, so I've started using firefox and changed my skin to a much, simpler one.

Now back to my topic, I realised that different parts of the bar will cause the ball to go in different directions, like if the ball hits the center, it's rebounding angle from the normal will the equal to the original angle at which the ball attacked th normal. If it hits the bar at 1/4 from the left or right, the rebounding angle from the normal will be the original angle from the normal plus half of it in the same direction. Therefore,

If the angle at which the ball hits the bar from the normal is x,

The rebounding angle from the normal is y,

The distance from the center at which the ball hits the bar is z in terms of fraction of the bar's length,

Hitting the center,

x = y,

Hitting 1/4 from the left or right,

x + 1/2x = -y,

I hereby conclude that,

x + 2xz = -y,

y = -x - 2xz,

for the case of the ball hitting the same side of the bar as it's direction,

and,

y = x + 2xz,

for the case of the ball hitting the opposite side of the bar of it's direction,


Summarizing, the angle from the normal at which it rebounds is equals to the negative of the addition of the angle at which the ball hits the bar from the normal and the double of the product of the angle at which the ball hits the bar from the normal and the distance from the center at which the ball hits the bar in terms of fraction of the bar's length in the case of the ball hitting the same side of the bar as it's direction. The angle from the normal at which it rebounds is equals to the addition of the angle at which the ball hits the bar from the normal and the double of the product of the angle at which the ball hits the bar from the normal and the distance from the center at which the ball hits the bar in terms of fraction of the bar's length.

So if a mathematical genius comes across this post and understands it, he will be able to own the game by applying the formula in approximately half a second to every single time the ball rebounds,,
spoke at : 12:07:00 AM