# Javelin Problem: Optimal Angle & Speed

• Skipe_
In summary, the conversation discusses the calculation of the optimal starting angle for throwing a javelin 90m without taking air resistance into consideration. The discussion includes defining the optimal starting angle as the angle that gives the greatest horizontal distance and mentions the need to prove this result instead of assuming it. The conversation also suggests solving for the angle that maximizes the range of a projectile.
Skipe_

## Homework Statement

A javelin is thrown 90m in an optimal starting angle. Air resistance is not taken into consideration. a) What is the optimal starting angle? b) At what speed does the javelin fly from the thrower's hand?

## The Attempt at a Solution

I really have no clue on this one. Is the optimal starting angle 45°? That would seem somehow logical.

Skipe_ said:
I really have no clue on this one. Is the optimal starting angle 45°? That would seem somehow logical.
I suspect they want you to derive the optimal starting angle, not just assume it. I assume they mean 'what is the angle that gives the greatest horizontal distance'. This is also called the range of a projectile. But they could mean something else. How does your book define 'optimal starting angle'?

Yes, i understand what it means. I just don't understand how you can calculate it range being the only given variable.

Skipe_ said:
Yes, i understand what it means. I just don't understand how you can calculate it range being the only given variable.
If by 'optimal starting angle' they mean 'the angle that gives the greatest horizontal distance', then calculating that has nothing to do with the distance. It's a general result. Your 'logical' guess was correct, but now you must prove it.

This seems like an odd thing to ask as part of a problem, since it's such a general result. What book are you using?

In any case, assuming some unknown speed v and some initial angle theta figure out the range of a projectile. Then solve for the angle that maximizes that range.

Also, the speed of the javelin would depend on the strength and technique of the thrower, so it is not possible to determine the exact speed without more information. However, in general, a higher initial speed would result in a longer throw.

I would approach this problem by first gathering more information. The optimal starting angle and speed of a javelin throw depend on several factors, including the aerodynamics of the javelin, the strength and technique of the thrower, and the environmental conditions (such as wind speed and direction).

To determine the optimal starting angle, we would need to conduct experiments or simulations using different angles and measure the distance of the throw. This would allow us to plot a graph and determine the angle that results in the longest throw. It is possible that the optimal angle may not be exactly 45°, as it may vary depending on the specific javelin and thrower.

Similarly, to determine the speed of the javelin, we would need to conduct experiments or simulations using different initial speeds and measure the distance of the throw. This would allow us to plot a graph and determine the speed that results in the longest throw. Again, this speed may vary depending on the specific javelin and thrower.

It is also important to note that air resistance is not taken into consideration in this problem. In reality, air resistance would have a significant impact on the optimal angle and speed of the throw. To accurately determine the optimal angle and speed, we would need to take into account the aerodynamics of the javelin and the environmental conditions.

In conclusion, as a scientist, I would need more information and data to provide an accurate answer to this problem. Conducting experiments or simulations and considering factors such as aerodynamics and environmental conditions would be necessary to determine the optimal angle and speed for a javelin throw.

## 1. What is the Javelin Problem and why is it important?

The Javelin Problem refers to the mathematical optimization of the angle and speed at which a javelin should be thrown in order to achieve the maximum distance. It is important because it allows athletes to improve their performance in javelin throwing and can also be applied to other similar sports or real-life situations.

## 2. What factors influence the optimal angle and speed in the Javelin Problem?

The optimal angle and speed in the Javelin Problem are influenced by several factors, including the weight and design of the javelin, the athlete's strength and technique, and environmental conditions such as wind speed and direction.

## 3. How is the optimal angle and speed determined in the Javelin Problem?

The optimal angle and speed in the Javelin Problem can be determined using mathematical equations and principles of projectile motion. These calculations take into account the factors mentioned above and aim to find the combination of angle and speed that will result in the longest distance traveled by the javelin.

## 4. Can the optimal angle and speed change for different athletes and situations?

Yes, the optimal angle and speed can vary for different athletes and situations. Each athlete may have different strengths and throwing techniques, which can affect the optimal angle and speed. Environmental conditions can also play a significant role in determining the optimal angle and speed.

## 5. How can the Javelin Problem be applied in real-life situations?

The principles of the Javelin Problem can be applied in various real-life situations, such as designing projectiles for military use or optimizing the trajectory of a rocket. It can also be used in sports other than javelin throwing, such as baseball or football, to determine the optimal angle and speed for throwing or kicking a ball.

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