Can any maths boffins help me calculate which goal is faster?

horsechoker

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I'm terrible at Maths but is it possible which goal was technically faster if scored over the same distance?

I plugged the two fastest in a calculator to calculate the speed in miles per hour

1 Gavin Stokes 2017 Maryhill v Clydebank 3–0

2.1 sec

This match was a junior (non-league) match involving two teams from the West of Scotland Super League First Division in Scottish football. Distance from the halfway line was approximately 46 metres.

(speed = 48.9996 miles per hour)


2 Vuk Bakic 2012 GSP Polet v FK Dorćol 4–1

2.2 sec [5]

[6]This match was a junior match of the Serbian 2. League. Immediately after the referee whistled the beginning of the meeting, Vuk Bakic sent the ball into the goal. Distance from the centre and goal was approximately 50 metres.

(speed = 50.8395 miles per hour)

The first is quicker in terms of time but the second is quicker in terms of velocity but if the distances were equal which one would have actually been faster?

Is the second one faster in terms of velocity because of the longer distance it travels? (because it can gain more speed?)
 
horsechoker said:
The first is quicker in terms of time but the second is quicker in terms of velocity but if the distances were equal which one would have actually been faster?
Click to expand...


Divide the speed of the first 1 by 21 then multiply that number by 22?

If it's lower than the speed of the second one it would have been slower, higher it would have been faster.

I think.

Edit: no that's completely wrong, I didn't think about it. Ignore this. :lol:
 
Chipper said:
Divide the speed of the first 1 by 21 then multiply that number by 22?

If it's lower than the speed of the second one it would have been slower, higher it would have been faster.

I think.

Edit: no that's completely wrong, I din't think about it. Ignore this. :lol:
Click to expand...
I followed your instructions anyway and got

51.332908

But if it's not the correct way to calculate it then it's not relevant

giggs-beckham said:
2.1 seconds is faster than 2.2 seconds
Click to expand...
Thanks Michael
 
You'd have to something to comvert mph into metres per second first for each shot.

Then you'd have to do something to equal out the two shots as if they were the same distance.
 
horsechoker said:
I followed your instructions anyway and got

51.332908

But if it's not the correct way to calculate it then it's not relevant
Click to expand...

Yes, that won't be right.

You'd have to something to convert mph into metres per second first for each shot.

Then you'd have to do something to equal out the two shots as if they were the same distance.
 
Bloody hell, just realised. The faster speed/velocity one will always be quicker if they were to travel the same distance.

:lol:

If you're driving 50 mph you'll cover the same distance in less time than if you're driving at 48mph, 40mph, or 25 mph. Doesn't matter what the distance is and applies here too.
 
In fact, this is an easy one: the shot with higher speed will be first on target if at equal distance. So its number 2.
 
I don’t really understand what the question is here? If you correct for distance, the faster one will be……well faster? You corrected for distance by calculating the speed. So the second one. 48.9mph or 21.9 m/s vs 50.8 mph or 22.7 m/s.
 
Short answer, 2 Vuk Bakic 2012 GSP Polet v FK Dorćol 4–1

The faster ball will reach the goal from the same distance.


The longer...
The speed you have over there is the average speed across the entire distance it travelled. The speed of the ball is the highest the moment it leaves the boot of the player. It then loses speed as it travels due to air friction, how quickly it loses speed depends on the surrounding air humidity, wind speed, ball aerodynamics etc. That means if we move the second goal to 46m instead of 50m the average speed will be higher than 48.9996mph. And if we move the first goal from 46m out to 50m the average speed would be a less than 50.8395mph. By how much we wouldn't know unless we know the exact conditions but it shouldn't be much unless there is strong wind involved.

Since both goals were scored from similar distance(4m is small in the context), we assume the average speed doesn't change much and equal conditions. The time recorded for the goal would be:
When shot from 46m
1) 2.1s (as before)
2) 2.024s

When shot from 50m
1) 2.2826s
2) 2.2s (as before)

Assuming equal conditions and being shot from the same distance, the faster ball will reach cross the goal line first assuming the keeper doesn't get a hand to it. 2 Vuk Bakic 2012 GSP Polet v FK Dorćol 4–1
But if we changed the question to:
Which goal took the shortest amount of time? The first goal (2.1s)
 
giggs-beckham said:
The ball will always be slowing down
Click to expand...
The ball accelerates away from the boot that kicked it (as its either stationaryor idling) , until it reaches peak velocity.

This is quite a short phase compared to the deceleration afterwards, but it's still incorrect to say a shot only slows down
 
RuudVNistelrooy10 said:
Short answer, 2 Vuk Bakic 2012 GSP Polet v FK Dorćol 4–1

The faster ball will reach the goal from the same distance.


The longer...
The speed you have over there is the average speed across the entire distance it travelled. The speed of the ball is the highest the moment it leaves the boot of the player. It then loses speed as it travels due to air friction, how quickly it loses speed depends on the surrounding air humidity, wind speed, ball aerodynamics etc. That means if we move the second goal to 46m instead of 50m the average speed will be higher than 48.9996mph. And if we move the first goal from 46m out to 50m the average speed would be a less than 50.8395mph. By how much we wouldn't know unless we know the exact conditions but it shouldn't be much unless there is strong wind involved.

Since both goals were scored from similar distance(4m is small in the context), we assume the average speed doesn't change much and equal conditions. The time recorded for the goal would be:
When shot from 46m
1) 2.1s (as before)
2) 2.024s

When shot from 50m
1) 2.2826s
2) 2.2s (as before)

Assuming equal conditions and being shot from the same distance, the faster ball will reach cross the goal line first assuming the keeper doesn't get a hand to it. 2 Vuk Bakic 2012 GSP Polet v FK Dorćol 4–1
But if we changed the question to:
Which goal took the shortest amount of time? The first goal (2.1s)
Click to expand...
Thank you

Unfortunately there doesn't seem to be footage of Stokes goal

 
Terrific Tangerine said:
The ball accelerates away from the boot that kicked it (as its either stationaryor idling) , until it reaches peak velocity.

This is quite a short phase compared to the deceleration afterwards, but it's still incorrect to say a shot only slows down
Click to expand...


Jein(yes&no) as a german would say.

But in cases like the OP, the contact time and acceleration time are incredibly small when compared to the rest(deceleration). Assuming instantaneous acceleration will still get you the "correct time" that matches exactly to every last digit and a couple more of any digital stopwatch.

I guess it's a case of are you asking an engineer or a physicist.
Even then I doubt a physicist would say it's incorrect but just not entirely correct.
Semantics
 
horsechoker said:
Thank you

Unfortunately there doesn't seem to be footage of Stokes goal
Click to expand...
Most welcomed.

On review, moving the goal 4m closer would probably result in a goal kick anyway. :lol:
Reminds me of my primary school days where every kickoff for my school team was just letting the lad with the strongest shot to have a go.
 
horsechoker said:
I'm terrible at Maths but is it possible which goal was technically faster if scored over the same distance?

I plugged the two fastest in a calculator to calculate the speed in miles per hour

1 Gavin Stokes 2017 Maryhill v Clydebank 3–0

2.1 sec

This match was a junior (non-league) match involving two teams from the West of Scotland Super League First Division in Scottish football. Distance from the halfway line was approximately 46 metres.

(speed = 48.9996 miles per hour)


2 Vuk Bakic 2012 GSP Polet v FK Dorćol 4–1

2.2 sec [5]

[6]This match was a junior match of the Serbian 2. League. Immediately after the referee whistled the beginning of the meeting, Vuk Bakic sent the ball into the goal. Distance from the centre and goal was approximately 50 metres.

(speed = 50.8395 miles per hour)

The first is quicker in terms of time but the second is quicker in terms of velocity but if the distances were equal which one would have actually been faster?

Is the second one faster in terms of velocity because of the longer distance it travels? (because it can gain more speed?)
Click to expand...

When distance is the same, then when the shots are taken the quickest moving ball scores first. To get ball speed divide distance by time:
First shot 46/2.1=21.9
Second shot 50/2.2=22.7
The units don't matter here as long you're comparing same to same. (In this case they're meters per second.)

So when kicked from the same distance the second shot goes in first as it is moving faster.

The second shot moves faster just because the ball was kicked harder, has a different trajectory, weather conditions, subtleties in ball design, etc, and has little to do with the distance it travels. The ball will slow down on the horizontal plane the further it travels but 4m won't make much of a difference.
 
Last edited:
Chipper said:
You'd have to something to comvert mph into metres per second first for each shot.

Then you'd have to do something to equal out the two shots as if they were the same distance.
Click to expand...

Chipper said:
Yes, that won't be right.

You'd have to something to convert mph into metres per second first for each shot.

Then you'd have to do something to equal out the two shots as if they were the same distance.
Click to expand...
Can any maths boffins help me calculate which one of these posts was faster?
 
Bright_Eyes said:
You don't even need to take into account the speed of the ball when calculating this, just the time taken for it to go in from kick off. If the first shot took 2.1s to go in and the second shot took 2.2s, the first shot was about 5% slower, so when kicked from the same distance the second shot goes in first as it is moving faster.

The second shot moves faster just because the ball was kicked harder, has a different trajectory, weather conditions, subtleties in ball design, etc, and has little to do with the distance it travels. The ball will slow down on the horizontal plane the further it travels but 4m doesn't make much of a difference.
Click to expand...
Time alone doesn't suffice if you don't consider the distance, or better: the relation of both, which is: the speed.
 
Terrific Tangerine said:
The ball accelerates away from the boot that kicked it (as its either stationaryor idling) , until it reaches peak velocity.

This is quite a short phase compared to the deceleration afterwards, but it's still incorrect to say a shot only slows down
Click to expand...
Eh?
So from the point it is no longer touching the boot, the only forces acting on it are drag and gravity. And you think it's going to carry on accelerating? How?

You should tell Newton so he can revise his laws of motion.
 
Math boffins would say:
x = sinθ + cosθ × πrad/g × ρe^x
Integrate velocity with respect to t
Divide by cross sectional area of the ball
Add 1 newton of drag per 3 percentage points of humidity
Conclusion: v2 > v1
 
BazzaBear said:
Eh?
So from the point it is no longer touching the boot, the only forces acting on it are drag and gravity. And you think it's going to carry on accelerating? How?

You should tell Newton so he can revise his laws of motion.
Click to expand...
Was the point I was making with the constant deceleration
 
giggs-beckham said:
Was the point I was making with the constant deceleration
Click to expand...
Not sure about that, but I think the ball is compressed, and accelerates with the decompression, similar to a spiral spring. The effect might be insignificant, but I think that's what he might refer to.
 
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