Question: How hard can a football be kicked

Martin Coath answered on 11 Jul 2024: last edited 11 Jul 2024 10:58 am

---

This sounds like it should be easy to get an very rough answer – but it isn’t! You would need to do a lot of research and sadly I am way too busy. But I can indicate how I quickly got a very rough answer below. Your maths teacher will be able to help you if you are really interested 😉

The world record for drop-kicking a football (soccer ball if you are reading this in the USA) is around 75m, and a standard ball has a mass of just over 400 grams or 0.4kg:

m = 0.4

Now you have to make a reasonable guess about the angle it was kicked at – lets say upwards at 45 degrees – and we will ignore the effect of the air on the ball.

I have not included the next calculation – look up ‘projectile motion’ to get the details – there are some good Youtube introductions.

But it is easy to show that for this distance the ball must have been moving at around 30 meters per second (over 60 miles per hour) after it was kicked:

v = 30

Now we can use a bit of simple standard maths to give us the force necessary to get that velocity:

F = (m*v)/(2*t)

put in the values we know to get

F = (0.4 * 30) / (2 * t)

We are nearly there – but using this approach we are now stuck because we have no value for t. This t stands for time – the time that the foot is in contact with the ball during the kick – this is pure guesswork!

How long are the foot and ball in contact during a kick? Let us just guess ‘one tenth of a second’ or:

t = 0.1

so now we can get some sort of answer:

F = (0.4 * 30) / (2 * 0.1) = 60

the answer is in Newtons – so the force on the ball is sixty Newtons – and that is how hard a ball can be kicked.

This argument is so full of holes you could use it to strain spaghetti! But anyone with a GCSE in maths can follow the calculations and improve on it.