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### Course: Algebra basics>Unit 8

Lesson 3: Pythagorean theorem

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

Sal uses the Pythagorean theorem to answer a question posed by a soccer superstar!  Created by Sal Khan.

## Want to join the conversation?

• Brazil adopted the SI system in the 19th century … so why?!
• Who is Tiago
• it's actually Thiago Silva. Brazil's and PSG's center-back and one of the best players on the earth
• Why is there to many assumes? Does that mean the answer will differ between the numbers that is assumed?
• Yes, the answers will differ dependant on some of the assumptions made. Some of these include: at how many mph the goalie can react (15 mph in video), the speed of the ball (60 mph in video), and the path of the ball (straight in video). Also, there were many circumstances Sal didn't take into account, such as height of the path of the ball and the starting position of the goalie (not all goalies stand at the direct center of the goal). Also it would be very rare that the shooter has the ability to kick the ball directly at the edge of the goal, so it would be possible the reaction time could be a bit slower (around 25 hundreds of a second) if the ball was closer to the starting position of the goalie. But then again, you have to give Sal some credit, as he wasn't provided with any specific information, thus forced to make the assumptions he made in the video.
• At , Sal draws the goalie stretched out towards to top right corner of the goal. However, in the real world, it would be extremely rare that a goalie would position him/herself directly in the center of the goalie (which would be exactly 12 ft. from each of the bottom corners of the goal, not including the width of the goalie), a circumstance Sal doesn't mention in the video. So, in conclusion, my question is: Roughly how much would the reaction time of the goalie differ, if he stands one foot towards the left of the goal, and the ball is kicked towards the right side area of the goal?
• This is not Thiago but I know a goog deal about soccer. So yes sals math is formatically correct however, this reasoning would never work because sal is not taking any consideration to other variables such as wind and the type of shot that is kicked. So yes the keeper could react after the ball is kicked however, in real life the keeper never reacts after the ball is kicked. The human body can not physically react to the ball and dive several feet to stop it this fast(which is 60mph on average but can reach up to 90mph). So the keeper has to react before the ball ever leaves the ground. They can only judge the kick by the kickers stance and positioning and they have to pick a side to dive before the kick even takes place. If you have ever watched professional soccer(premier league, bundesleague, la leaga etc.) you have seen the keeper dive to the wrong side time and time again because he simply picks the wrong side. The ball also can do many things in the air. The ball can have a spin in any direction and can be kicked where the ball drops at the last second and many other ways, it is very rare that the ball goes in a perfectly straight line. This is why sals reasoning impressive as it is would not work in real life. Don't mean to talk down about this video but a voice of experience is useful.
hope this helps vote up if you like my answer.
• I harbor such a great amount of disgust towards the System of measure used in this video that I just have to ask this question: Is it actually good for anything at all? Because if it isn't, I'll probably have to keep wondering why it is used so often. If it does have its advantages, then I would like to know them, for I must have been utterly ignorant of them.
• At Sal Khan says that going to the top right is the hardest to get to but I disagree because when you are standing you have a better chance of diving high then to dive low. When going to the bottom corner you have to get down and then dive. So even though the ball takes more time to travel to the bottom corner the time it takes to squat down decreases the reaction time for the goal keeper.
• At , Why does Sal use 5280 ?.
• Because there are 5,280 feet in a mile.

1 mile = 1,760 yards and 1 yard = 3 feet. Then apply unit analysis.
• Can Sal mathematically determine the most efficient formation to cover the most area on the field?