The maths behind fireworks night

The 5th November is Guy Fawkes Night, traditionally spent standing out in the cold, exclaiming "Oooooooo!" and "Ahhhhhhhh!" as fireworks enliven the night's sky.

But do you know how fireworks actually work (and how much maths is involved)?

When a firework is lit, a chemical reaction launches the shell into the air. If everything works as it should, this shell then bursts, scattering the content across the sky ("Oooooo!").

You can replicate the motion of the firework with a tennis ball; when you throw the ball into the air you'll notice that the ball rises and starts to fall again, once it has reached a certain height.

If you throw it at an angle, it goes farther out, and if you throw the ball straight up, it will reach a higher point. This trajectory is determined by physics which dictates that the path an object takes when it is launched into the air will be a curve.

Here's the maths part: every curve has an equation associated with it that describes all sorts of elements related to the curve, including how wide and tall it is.

This equation is vital for fireworks as, if not launched at the correct angle, the firework could explode at the wrong moment or could land in the wrong location. This magic number depends on the firework in question.

The heavier it is, the greater the force needed to propel it into the air and get it to the right height.

Here's the second maths part: these equations are always quadratic, which means that one part of the equation must be squared. The standard form for a quadratic equation is as follows: