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Mathematics In Golf

A look into how Golf uses Math
by

Michael Zuo

on 7 June 2011

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Transcript of Mathematics In Golf

Mathematics in Golf Math is used in virtually all sports, in fact everything in our society uses math in one form or another. Statistics, Score keeping, Hitting, Putting, even just playing Golf requires math Sometimes a good understanding of math is all that seperates you from getting 18 hole-in-ones and hitting the ball into the sand every time. The first application would the be the calculation of scores, after all without scores how do you determine who wins or loses??? Birdies, hole-in-ones, eagles, bogeys, Albatross, Par +/- Each hole in an 18 hole course has a specific shot limit, so if hole #7 was designed to be completed in 5 shots, and you do it in 10 hits, you would be a bad golfer and have a score of Par +5 Whoever has the lowest amount of shots total across all 18 holes, is the winner, so for example:
Hole #1: 2
Hole #2: 4
Hole #3: 1
Hole #4: 7
etc..... Positioning is everything in golf, positioning of your body, positioning of the club, positioning of the golf ball, position of the putting green, positions of the sand traps, positions of the trees, position of the hole, even your own position effects the difficulty and probablitiy of a shot succeeding For example if you can't aim and somehow get the golf ball into a sand trap, the probability of you getting a birdie (one under par, the amount of shots the hole was designed for) is very slim.
Likewise if you are the next Tiger Woods and get the ball on to the putting green (the area around the hole) in one shot, the chances of you getting it under par is very high. 1. Basketball is a worldwide sport where players needs to score points by throwing or shooting a ball through the top of a basketball hoop. 2. Basketball is a team sport in which players need passing, shooting, rebounding, dribbling and blocking skills. We’re focusing on shooting in basketball which involves the quadratic formula for solving a parabola. 3. In a basketball game, people don’t just calculate the scores, wins, and loss.
They also calculate the player’s statistics 4. In addition, there are some calculation for the path of the ball. 5. Q: In a three point contest, players have to score 10 three point ball. The path of the basketball after it is thrown from a height of 2.3m above the ground is given by the equation :
“H= -0.25d ² + 2d +2.3”, where h is the height of the ball, and d is the horizontal distance, in meters. Find the distance when the ball goes in the hoop when the hoop is 3 meters When the basketball goes in the hoop, the height is 3 meters.
Therefore, let h= 3
-0.25d ² + 2d +2.3 = 3
-0.25d ² + 2d - 0.7 = 0
D = -b ±√b ² - 4ac
2a
= -2 ± √ 2²- 4 (-0.25)(2.3)
2(-0.25)
= -2 ± √ 4 + 2.3
- 0.5 -2 + √ 6.3 -2 - √ 6.3
-0.5 -0.5
= - 1 = 9 Since d represents the distance, so it cannot be negative. Therefore, The basketball is at the distance of 9 meters when it goes in the hoop Equations As you can see on the graph, there are 10 different golf balls and
you have to find which linear equations can knock the golf ball into
the tee.
Many real life golf situations will require an extensive understanding of parabolas to get the ball into the tee with the least amount of shots, such as caluclating the optimal angle at which you should hit the ball and the optimal speed at which you can hit it, to either maximise the distance the ball travels or to make it travel to a specific location. To find the equations for these golf balls, I will use the simplest method, slope-intercept form or y = mx + b, including rise/run. However, linear equations are used once the golf ball is on the putting green, the area surround the tee, because launching the ball into the air when it's only 2 meters away from the hole is not a good idea! For example to get golf ball number 8 into the hole, I see that it is 6 units away on the y axis
and 6 units away on the x axis, (4, -4) relative to (-2, 2) So it will have a rise/run of 6/-6
= -1
Also it will have a y intercept (b) of 0
Therefore the equation will be
y = -1x + 0
or y = -x Now for a parabolic equation it gets harder because a golf ball doesn't fly in a perfect parabolic arch, instead because of the dimples on the golf ball it uses something called the magnus effect which is university level math, so obviously I cannot give an example. However, I can calculate how far a golf ball will travel in a given period of time, or how long it will take for a golf ball to reach x distance, using the following formula:

d = (vcosm)t

where d = distance
v = initial velocity
m = launch angle
t = time So if Bob goes to his local golf course records his practise sessions, and these measurements are recorded:
initial velocity = 70 m per second and launch angle of 30 degrees on average.
How far did the ball travel 5 seconds after his swing?

To solve, I will use the formula d = (vcosm)t

d = (70cos30)5
d = (60.6218)5
d = 303.1 m

The ball travelled 303.1 m 5 seconds after his swing Mathematics in Basketball Mathematics in Soccer Mathematics in Sport As you can see, math is very useful in golf, and all professional golfers use math in some form or another to get an advantage over their competitors. In fact, it would be very difficult to play golf at all if you don't know math! One can see that a soccer field has shape of rectangles and circle. One can use these two shape and relate to a soccer field and make a problem that involved in soccer for those who are interested In soccer, people can form a triangle and square to pass the ball and get through the other team and score. Soccer is the most popular sport around the world
A soccer ball can form a parabola with a kick
For example:

The path of a soccer ball is modelled by the relation h= -1/4 (d-18)2+30, where d is the horizontal distance, in metres, after it was kicked, and h is the height, in metres, above the ground One can also use triangles to make a question in soccer
For example:

If a soccer player is in angle A and runs to angle B, what is the distance the player needs to run if angle A is 51 degrees and BC is 10m To solve this we can use the sin ratio.

SinA = opposite/hypotenuse
Sin51 = 10/h
h = 10/sin51
h = 13 meters If a baseball is batted at an angle of 30 degrees, to the ground, the distance the ball travels can be estimated using the equation d = 0.0034s^2 + 0.004s - 0.3, where s is the bat speed, in kilometres per hour, and d is the distance flown, in metres. At what speed does the batter need to hit the ball in order to have a home run where the ball flies 125m? Round to the nearest tenth FINAL QUESTION Math in Baseball Math is used in many ways in baseball for example for calculating being able to count to three outs or nine innings or add up. You can also calculate the amount of force needed to apply to the ball to make it go a certain, desired distance. You can also calculate the time it takes for a certain player to steal a base, and see if it can be done quicker than the catcher can get the ball to that base, etc. You can also calculate the height of the arch created by the ball's path of travel. So to start there is batting statics like 1B which is the ability to determine if the batter could reach the first base without the contribution of a fielding error. And there is 2B and 3B which basically means getting 2nd and 3rd base without any error. There is also BA which calculates batting average (divide hits by batting appearance). You could determine the least amount of force needed to hit a ball out of the stadium (the least amount needed just to clear the fence). You can calculate the velocity of the players, the ball, etc.
Sabermetrics is the analysis of baseball through objective, empirical evidence, especially baseball statistics that measure in-game activity rather. Say you are batting for the Baltimore Orioles. You step up to the plate for the 60th time this season. Here comes the pitch... home run! It's your 20th hit of the year. What's your batting average? To find out, divide the number of hits by the number of at-bats: 20 hits ÷ 60 at-bats = .300
There is also many other forms of statics that are used in baseball to evaluate the skills of baseball player. Like for example there is base running statics, fielding statics, general statics. The baseball is hit from position A and its maximum height is B and its hits ground. A good baseball player tries to make that ball land as far as possible. To do that you have to take many things in mind, like for example Gravity is always pulling downwards on the ball. If you hit the ball straight up, it spends quite a bit of time in the air, but doesn't travel far from home plate. If you hit the ball horizontally, as in a line drive, the ball moves away from home plate at maximum velocity, but quickly hits the ground because of gravity -- still not very far from home plate. . To maximize your hitting distance, you need to have both a high horizontal velocity AND you need to keep the ball in the air for a longer time. You can do this by hitting the ball at an upward angle The distance a baseball travels depends on two primary factors: the angle at which the ball leaves the bat, and how fast the ball is hit. The speed of the ball depends on both the speed of the pitch and the speed of the bat. If the bat is standing still and the ball hits it, the ball will bounce off the bat with most, but not all, of the pitch speed. (Some of the energy is wasted in the friction of deforming the ball, making a sound, etc.) If the ball is standing still and is hit by the bat, it's given a good portion of the bat's speed. Combine the two and you can see that a pitched ball hitting a swinging bat gains a good portion of the sum of both the pitch and the bat speed. Batting Statistics
Statistic Top5 Best
BA .321 .372
HR 37 58
RBI 124 156
SLG .571 .812

Pitching Statistics
Statistic Top5 Best
CG 3 9
ERA 3.19 1.87
G 77 94
GS 34 35
IP 225.1 255
K 206 290
SHO 2 5
SV 38 62
W 17 22 In any game, the equipment player’s use determines the way the game unfolds. Try to imagine a soccer game played with an American football! Or try playing tennis with the wooden racquets of thirty years ago. Change the equipment, and you discover a very different game. As part of our look at baseball, we decided to examine the tools of the baseball trade: bats, balls, and gloves. Perhaps the most crucial and visible tool in baseball is the bat. A bat is the offensive weapon, the tool with which runs are scored. The Question

A baseball just hit the ball. The ball comes out of the bat at an initial speed of 59 meters per second. The equation is H= -16t^2+59t+1.5 represent the height in H and the time T the ball is in motion. How long did it take the ball to land? Examples would include calculating the distance of a golf shot, the place where it landed, the height the ball reached in flight, as well as calculating the angle at which to hit the ball and the speed at which to hit the ball. Furthermore math can be used to determine the optimal play so you can minimise the amount shots you have to take. 0 = -16t^2+59t=1.5

D=-b±√b^2-4ac
2a

D=-59±√59^2-4(-16)x1.5
2(-16)

D=-59±59.8-32

D=-59+59.8
32
=-0.025

D=-59-59.8
-32
=3.7

Since the time cannot be negative, so it will take 3.7 seconds
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