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Current time:0:00Total duration:12:05

Thiago asks: How much time does a goalkeeper have to react to a penalty kick?

Video transcript

what the temple will leave my hands you want a bunch of details what stages one stampede a fish pretty good great question Thiago and to understand it let's look at the dimensions of a penalty kick the kick itself is from 12 yards away from the goal or 36 feet the goal itself is 24 feet wide or 8 yards wide and the goal is 8 feet tall and so let's think about a few other dimensions that might not be as obvious let's try to figure out the distance from the ball where it's kicked to the bottom right of the goal and this obviously is going to be the same distance as to the bottom left as the bottom left of the goal and I encourage anyone watching this to pause the video and think about that right now well the way I've drawn it you see that this is actually this is actually a right triangle and so we could use the Pythagorean theorem in order to figure out what is this distance right over here you might say well how do we figure that out well we already know that this this length of the triangle is 36 feet and we know that this base right over here is half of the width of the goal so this is going to be 12 feet right over there so the Pythagorean theorem tells us that the distance this distance right over here is going to be the square root of the square of the sum of the squares of the other sides so it's going to be the square root of 12 squared plus 36 squared and let's get our calculator out and try to answer it and figure out what that is so that's going to be the square root of 12 squared plus 36 feet squared whoops not 33 36 feet squared is equal to 37 point 9 so let's just say well let's just use that number right now so 37 point we can even say point 9 5 almost 38 feet so this is this is approximately equal to approximately equal to 37 point nine five feet and that's going to be the same as this distance right over here now let's figure out the distance and even further distance a distance to the top right which is also going to be the same thing as the distance to the top left and encourage once again people to pause the video and try to think about that on their own well let's draw another right triangle and this one might not be as obvious but if I draw the straight line distance of the ball - in this case the top right of the goal I have now constructed another right triangle notice this is a 90-degree angle one side is thirty nine thirty seven point nine five feet the other side is eight feet tall and so this distance this distance right over here is going to be the square root the square root of thirty seven point nine five squared thirty seven point nine five squared plus eight feet squared plus eight squared so let's figure out what that is the calculator out so I can square the last entry on my calculator just by typing this that just means take the last answer square it and then add that to eight squared which we know is 64 and now we want to take the square root of that so take the square root of 1504 gets us to 30 set 38 we'll just say roughly thirty eight point eight feet or let's say seven eight feet so this is approximately equal to 38 point seven eight feet now the next thing I want to think about and I think this will be what we focus on to figure out how much time does the goalie have to get here because one could argue that this is the hardest to get to that the goalie has to DA to have to travel the farthest and they have to dive for this right over here so let's think about the distance from this point to this point here and then we can think about how much the goalie actually has to move because they have some height in their hands they can stick up in the air and this one once again is a fairly straightforward Pythagorean theorem problem you have a right triangle here you could also see it on this side it's a little easier you have you have a right triangle here we know this is 12 feet and that this is right this right over here is 8 feet so we know that this distance right over here is going to be the square root of 12 feet squared which is 144 plus 8 feet squared which is 64 so let's figure out what that is so that's going to be the square root of 144 144 plus 64 is equal to fourteen point four two feet it's equal to fourteen point four two feet now we assume that the person the the goalie isn't traveling all the way from here to all the way there the goalie has some height and he or she could stick their hands up in the air so we could imagine a goalie stretched out like this trying to dive for that ball and so the actual distance that they have to travel is from the tip of their reach from the tip of the reach to that corner right over there so if we assume that the the entire four goalie stretched out is a is let's say seven and a half feet completely stretched out so this distance if this distance fully stretched out is 7.5 feet and they're trying to get to four and they're trying to get 14 point four two feet away and I could maybe around and start rounding down a little bit rougher numbers to say fourteen point four feet then they need to travel they need to travel about six point nine feet so they need to travel about six point nine feet so for this top right kick or this top left kick the ball is going to travel thirty is going to is going to travel thirty eight almost thirty nine feet thirty eight point eight thirty eight point seven eight feet and the goalie has to travel the goaltender has to travel six point nine feet now that we know the distance is that the ball has to travel and that the goalkeeper has to travel we can now think about the time in which it's going to happen and to do that we're going to have to make assumptions about their speed so I did some research on the internet and it looks like a penalty kick can can go a fast pedal kick kick can be around 60 miles per hour although it does look like they're documented cases of 80 miles per hour or even higher than that but let's just say 60 miles per hour for a fast penalty kick so this is the kick speed or the ball speed ball speed and let's assume that this person can jump at 15 miles per hour which is actually a pretty good speed from a standstill so it actually might be a little bit aggressive so jump speed I'll write it here jump speed jump speed of the goalkeeper let's write that as 15 miles per hour and so to make sense of it because everything else we've done in feet let's convert these in each into feet so 60 miles per hour if I want to convert it to feet we just have to remind ourselves that 60 60 miles is the equivalent to 60 times 5,280 feet 5,280 feet each each mile is 5280 feet so this would give me the total number of feet in an hour but we don't want feet per hour we want feet per seconds so an hour has this is how much how far you would go and feet in an hour to figure it out in seconds you would want to divide by 3600 because there are 3600 seconds in an hour so this gets us to 88 this gets us to 88 feet per second 88 feet per second for the ball and now let's do the same thing for the goalkeeper so 15 times 5280 5,280 so this is the feet traveled in an hour but we want it in a second so we're going to divide it by 3600 gets us to 22 feet per second so this is equal to 22 feet in a second 22 feet per second so now we can use the speeds to figure out how long will it take the ball to go from this point all the way to the top right corner well we just have to remind ourselves the distance is equal to is equal to speed times time or if we want the time we just have to take the distance and divide it I speed so the time for the ball so ball time is going to be equal to is going to be equal to 38 point let's just go thirty eight point eight feet thirty eight point eight feet I have to make a lot of rough assumptions here anyway is going to be equal to thirty eight point eight feet divided by eighty eight feet per second eighty eight feet per second which is equal to so thirty eight point eight divided by eighty eight it gets us point four four seconds so let's write that so that's zero zero point four four seconds or forty four hundredths of a second a little under half of a second for this ball to reach there obviously if the ball was going even faster it would take even less time if it's going slower it would take a little more time now let's think about how far it would take for this person to travel the six point nine feet so the goalkeeper time goal goalie time is equal to the six point nine feed we're assuming he's kind of already in this position kind of already starting to stretch out or he stretches out while he's in the air when when he launches himself so it's going to be said obviously I'm making a lot of rough assumptions here six point nine feet divided by 22 feet per second 22 feet per second so that gets us six point nine divided by 22 is equal to 0.3 one on this round there's zero point three one is equal to zero point three one seconds so just based on what we saw the ball is going to take for forty four hundredths of a second to get there the goalkeeper if we assume the 15 miles per hour is going to take thirty one hundredths of a second to get there and so they only have they only have the difference to make the decision where to jump and even frankly to start their drum getting into the jumping position to kind of scrunch up and jump a little bit so the difference between these two things is only we write this in a new color this is 13 hundredths of a second 13 hundreds of a second to make this decision and that's why frankly penalty kicks are successful so frequently most people's reaction time and even professional athletes does not professional athletes get close to this in terms of reaction time I did a little bit of research on the internet most other people's reaction time is nowhere near this this low it's often double this or or higher so even if they make the exact right decision and even if they're able to launch themselves up at 15 miles per hour they have a little over a tenth of a second to make that decision now once again I want to emphasize this was given all of these assumptions that I made you might want to lower or higher this assumption of how fast they can jump you might want to lower or you might want to increase or decrease the assumption about how fast the ball is going and you could also think about different points on the goal to see which one based on your assumptions might require different reaction times