# What Is the Optimal Kicking Angle for Maximum Distance in Football?

• Stephen Garner
In summary, the conversation discusses the best angle to kick a ball during kickoffs in order for it to go as far as possible. The given data is that the ball leaves the foot at a speed of 72 km/h, which is converted to 20 m/s. The conversation includes equations for calculating the x- and y-components of the initial velocity and suggests using an unknown variable to represent the angle. The speaker also advises to not plug in any numbers until the final step.
Stephen Garner

## Homework Statement

The school football team has asked you for advice. During kickoffs the ball is not going far enough. The team's kicker shows you his kicks, and you figure out that he consistently kicks the ball so that it leaves his foot moving at 72 km/h.

a) Predict the best angle for him to try to kick the ball so that it will go as far as possible. [a: 45 degrees]

## Homework Equations

Y-Component: sinΘ = opp/hyp

## The Attempt at a Solution

I have converted 72 km/h to m/s.

72 * 1000 = 72000 / 3600 = 20m/s

I am confused because course has not asked us to predict an angle given such little data. Am I suppose to use gravity somewhere in here? I don't know how they arrived at 45 degrees.

How long will the ball be in the air? How far in the x-direction does it travel in that time? (Both as functions of the angle)

How do I figure out X-component if I don't have the angle though?

Stephen Garner said:
How do I figure out X-component if I don't have the angle though?
You write it as a function of the angle.

f(x) = 20x?

Stephen Garner said:
f(x) = 20x?
No. Create an unknown to represent the angle. θ would be a standard choice.
Write the initial velocity components in terms of that.
Style tip: ignore the given speed of 20m/s for now. Just call it v. There are many advantages in not plugging in any numbers until the final step.

what numbers am I plugging into what? I'm more confused than before. x + y = 180?

Stephen Garner said:
what numbers am I plugging into what? I'm more confused than before. x + y = 180?
If the kicker kicks the ball at a speed v and an angle θ to the horizontal, what are the vertical amd horizontal components of its initial velocity?

## 1. What is the "Predict best angle problem"?

The "Predict best angle problem" is a mathematical problem that involves determining the optimal angle for a projectile to be launched in order to achieve a specific distance or target. It is commonly used in fields such as physics, engineering, and ballistics.

## 2. How is the "Predict best angle problem" solved?

The "Predict best angle problem" is typically solved using mathematical equations such as the range equation or the projectile motion equations. These equations take into account factors such as launch angle, initial velocity, and gravitational force to determine the optimal angle for a given scenario.

## 3. What are the applications of the "Predict best angle problem"?

The "Predict best angle problem" has various applications in real-world situations, such as designing the trajectory of a rocket launch, optimizing the angle of a ski jump, or calculating the perfect angle for a basketball shot. It is also used in military operations for determining the most effective launch angle for missiles or projectiles.

## 4. Are there any limitations to the "Predict best angle problem"?

Like any mathematical model, the "Predict best angle problem" has some limitations. It assumes ideal conditions and does not take into account factors such as air resistance, wind, or other external forces that may affect the trajectory of a projectile. Additionally, the problem may become more complex and difficult to solve when dealing with non-uniform terrains or objects with irregular shapes.

## 5. Can the "Predict best angle problem" be solved using computer simulations?

Yes, the "Predict best angle problem" can be solved using computer simulations by inputting the necessary parameters and running the simulation multiple times to determine the optimal angle. This allows for more accurate and precise results, taking into account various factors that may affect the trajectory of the projectile. However, it is important to note that the accuracy of the simulation depends on the accuracy of the input parameters and the assumptions made in the model.

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