Why does leaning back make a kicked ball go higher? It's relatively common knowledge that when one kicks a football, if they lean back the ball usually goes higher, and if they lean forward slightly it goes at a more desirable height.
Why does leaning back make the ball go higher?
I'm guessing that it could be something to do with the centre of mass or angular momentum.
 A: When lean back you're foot naturally goes a little bit higher. Try it, just lift one foot like 5 cm of the floor, and then tilt back and forth and you will see that you're foot will go along. When you hit a football every mm counts.  
A: Your leg moves within certain angles of displacement - back and forth - with respect to your torso (which the leg is "mounted to"). 
On the other hand, the angle the ball will go (the hight above the court) depends on the angle your leg assumes at the last moment of contact (the greater the angle, the higher above the ground the foot goes and the higher the ball will go).
Now, if you lean back, the same movement of your leg - wrt. your torso - will result in your foot going higher above the ground (notice that if you are just lying back on the ground and kick the ball, you will find it impossible to kick a ball in parallel to the ground unless you kick it with only the tip of your shoe - if you kick the ball with the upper part of your foot the ball will always go up).
To sum up - leaning back changes the angle of your torso with respect to the ground, which changes the hight your foot will naturally go when kicking the ball, which makes it go higher.
By the way - how high the ball goes depends also where, relative to your body, the ball is at the moment of kicking. If it is just next to your leg you are standing on, it will tend to go low above the ground, but if it is further in front of you it will rather go higher. This is so for the same reason as your initial question - angle.
A: I think it's all in the geometry. Let's first assume that knees don't rotate, and our legs are stiff straight. Consider the rotation of your leg about your hip and focus on the trajectory of the kicking foot, some sort of circular arc. Think of it as a pendulum.
If you kick standing vertically above the ball, you will hit the ball with your foot at the very bottom of the pendulum's cycle, the lowest point. It's like dropping the pendulum onto a ball that is placed right beneath the axis of rotation. On impact, the pendulum's velocity is horizontal.
If you lean back, your hip will move horizontally away from the ball, or the pendulum's axis is moved away from the ball. When dropped, the pendulum will not hit the ball at the lowest point but at a "later" point in the movement, and the impact velocity will have a vertical component.
Add this : if you think of the ball not as a point mass (which is in fact compulsory since your hip moving away means you will hit the ball in a different place on its surface since your leg hasn't stretched), then the pendulum hits the under side of the ball towards the sky when ball is not right below, whereas it will hit it higher and slightly towards the ground if the ball is placed under it.
I think that accounting for knee rotation doesn't make much difference.
Why does leaning forward guarantee not only a lower shot but also a better controlled one ? I have a vague idea about this, as a casual football player, nothing to do with physics or biomechanics. I would say that when you lean back, you let physics do the work, swinging your leg about your hip, whereas when leaning forward it feels to me like there is less swinging and more voluntary muscular action.
