# Projectile Motion Quarterback Throw

• wizzpowa
In summary, the task is to determine the speed at which a quarterback must throw a football in order to cover a horizontal distance of 193 m, given that the ball is launched at a low angle of 32.1 ° above the horizontal and air resistance can be ignored. The comparison is made to a baseball pitcher who can throw a fastball at 45 m/s. The relevant equations are the Kinematic equations. To solve this problem, it may be helpful to experiment with different initial speeds and observe the resulting range and hang time of the ball. This may provide insight on how to approach the original claim.
wizzpowa

## Homework Statement

A quarterback claims that he can throw the football a horizontal distance of 193 m. Furthermore, he claims that he can do this by launching the ball at the relatively low angle of 32.1 ° above the horizontal. To evaluate this claim, determine the speed with which this quarterback must throw the ball. Assume that the ball is launched and caught at the same vertical level and that air resistance can be ignored. For comparison a baseball pitcher who can accurately throw a fastball at 45 m/s (100 mph) would be considered exceptional.

## Homework Equations

The Kinematic equations

## The Attempt at a Solution

So I can't figure out how to get anywhere with only the few variables they give me. I can only figure out how to get the initial speed in both the x and y directions. What should I do?

wizzpowa said:

## Homework Statement

A quarterback claims that he can throw the football a horizontal distance of 193 m. Furthermore, he claims that he can do this by launching the ball at the relatively low angle of 32.1 ° above the horizontal. To evaluate this claim, determine the speed with which this quarterback must throw the ball. Assume that the ball is launched and caught at the same vertical level and that air resistance can be ignored. For comparison a baseball pitcher who can accurately throw a fastball at 45 m/s (100 mph) would be considered exceptional.

## Homework Equations

The Kinematic equations

## The Attempt at a Solution

So I can't figure out how to get anywhere with only the few variables they give me. I can only figure out how to get the initial speed in both the x and y directions. What should I do?

Check out what range and "hang time" you get for a ball thrown at 10m/s, and also 20m/s to get a feel for what the ball does.
Once you have done that it may become obvious how to approach the original claim.

## 1. How does the angle of release affect the distance of a quarterback's throw?

The angle of release plays a crucial role in the distance of a quarterback's throw. Generally, a higher launch angle will result in a longer throw. This is because a higher angle allows the ball to stay in the air for a longer period of time, giving it more time to travel downfield. However, if the angle is too high, the ball may come down at a steeper angle, resulting in a shorter throw. It is important for a quarterback to find the optimal angle of release for each throw.

## 2. What factors can affect the trajectory of a quarterback's throw?

Several factors can affect the trajectory of a quarterback's throw, including the angle of release, the initial velocity, and the air resistance. The angle of release and initial velocity determine the path of the ball, while air resistance can slow the ball down and alter its trajectory. Other factors such as wind and the release point of the ball can also impact the throw's trajectory.

## 3. How does the weight of the football affect a quarterback's throw?

The weight of the football can have a significant impact on a quarterback's throw. A heavier football will require more force to be applied by the quarterback to achieve the same distance as a lighter football. This can also affect the accuracy of the throw, as a heavier ball may be more difficult to control. Quarterbacks often have a preference for the weight of the football they use, and they must adjust their throws accordingly.

## 4. Can a quarterback's throw be affected by external forces?

Yes, external forces such as wind and air resistance can have a significant impact on a quarterback's throw. A strong wind can alter the trajectory of the ball, making it more difficult for the quarterback to accurately throw to their intended target. Additionally, air resistance can slow the ball down, resulting in a shorter throw than intended. Quarterbacks must take these external forces into account when making their throws.

## 5. How can quarterbacks improve their accuracy and distance in their throws?

Quarterbacks can improve their accuracy and distance in their throws through practice and training. This includes working on their throwing mechanics, such as footwork and arm motion, to achieve a more efficient and powerful throw. They can also improve their strength and conditioning to increase their throwing power. Additionally, studying and understanding the principles of projectile motion can help quarterbacks make more precise throws by adjusting their release angle and velocity.

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