There’s a lot of math behind a simple game of golf that we don’t take into account – from the swing to the air temperature
Next time you play golf, you might not see a mathematician because you will likely lose.
It turns out that there is a lot of hidden math behind a simple game of golf that many of us are unaware of.
On a Tom Rocks Maths blog, math expert Sian Langham talks about how much math is in this popular sport, and it’s pretty mind-blowing.
Mathematicians can use equations to predict the exact trajectory of the ball and how certain factors can affect it.
Factors include the speed of the swing, air temperature, and even the quality of the golf ball itself.
On the blog, Sian said, “A golf ball in flight is an example of a projectile because it follows a curved path called a parabola.
“The shape of the curve is influenced by two main forces – gravity and air resistance.”
Now it’s time for the complicated part.
Since there is no air resistance, the horizontal speed of the golf ball remains constant during the flight, as no “external forces” occur.
She continued, “However, vertical speed is affected by gravity, so it changes over time. The acceleration due to gravity g is 9.8 m / s2.
“This acts on the earth so that the speed of an object decreases by 9.8 m / s every second when the object is moving upwards and increases when it is moving downwards.
“Suppose a golf ball is initially hit at a vertical speed of 49 m / s. This initially decreases with the upward movement of the ball and reaches zero after 5 seconds (9.8 * 5 = 49). “
If you want the ball to go up you need to make sure that the “vertical speed” is zero.
This is when the ball has reached its maximum height, and after that point the ball will move down towards the ground.
Basically, the angle at which the ball is hit affects the shape of the track.
Sian explained: “Assume that the golf ball is hit at speed U at an angle θ to the horizontal.
“This can be broken down into horizontal and vertical components using trigonometry.
“As you would expect, at a small angle, the golf ball has a large horizontal speed and a small vertical speed.
“That leads to a path with great reach but low altitude. If the angle is large, the opposite happens, and the path has a large height and a small range. “
Depending on the terrain and the type of shot, you have to decide which situation you need.
In terms of angle, the maximum height and reach is usually 45 degrees so be sure to write this down.
For those who want to get some real math, Sian explains how to calculate the height and speed of the ball.
She explained, “Vertical velocity can be measured fairly accurately using a set of equations called the equations of motion, or SUVAT equations.
“They are derived from a speed-time diagram, but are pretty easy to use.”
V = U + AT; V2 = U2 + 2AS; S = UT + AT2 / 2; S = (U + V) * T / 2
Simplified: “where S = displacement; U = initial speed of the object; V = final speed of the object; A = acceleration (usually g); T = flight time.
“These equations apply to both the vertical and horizontal components of speed.
“Suppose a ball is hit at an initial speed of 40 m / s at an angle of 30 degrees from the horizontal. We want to find out its maximum altitude, range and flight time. “
“Let’s first determine the initial horizontal and vertical speed. The horizontal speed in trigonometry is cos (30) * 40 = 34.6 m / s. The vertical speed is sin (30) * 40 = 20 m / s. “
Granted, this is the simplified scenario, but it’s a great way to analyze projectiles and consider the effects of drag.
In fact, golf balls were dimpled for this in 1905.
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