# A quarterback throws a football to a stationary receiver

• Etheryte
In summary, the conversation discusses finding the initial speed of a thrown football to reach a stationary receiver, as well as the highest point of the ball's flight. The problem involves two dimensions of motion, horizontal and vertical, and requires equations for each. The equations are then set equal to each other to solve for the initial velocity and time.
Etheryte
1. Homework Statement
A quarterback throws a football to a stationary receiver 31.5m away from him. If the football is thrown at an initial angle of 40° to the ground, at what initial speed must the quarterback throw the ball for it to reach the receiver? What's the balls highest point during flight?

2. Homework Equations

3. The Attempt at a Solution

I know this is only one small attempt at rearranging the formula, but trust me if you checked my trash you'd find crumpled up pieces of paper with many more attempts.

I always go through the same procedure;
1. I make my goal to find the initial velocity.
2. To find initial velocity, I need time.
3. To find time, I need /\y.
4. To find /\y, I need the initial velocity.

The motion has two dimensions: vertical and horizontal. Write the equations of motion w.r.t. time for both motions. The time that the football takes to reach its destination must be the same for both horizontal and vertical motions...

I'm sorry, but could you please explain more in depth? I know there's two dimensions but set what two motions with which equations?

Etheryte said:
I'm sorry, but could you please explain more in depth? I know there's two dimensions but set what two motions with which equations?
The horizontal motion and the vertical motion. What are the equations for each?

Oh, the /\y and /\x equations? I thought you referred to the x and y components of the velocity..

Well, after trying to set them equal to each other — it gets to a point where the /\t can't be really set equal to the rest of the /\y equation and you have a quadratic of a sort:

The x and y components of the trajectory are independent equations in terms of time. Write them separately to begin with. (And it would be better if you would type them in rather than attaching image. Use icons in the editing window's top bar to make subscripts or superscripts: x2, x2. Other symbols and special characters can be found using the Sigma icon).

You should then have a pair of equations that describe the motion with respect to time. The only unknowns will be the initial velocity and time. Two equations in two unknowns.

## 1. How does the quarterback throw a football to a stationary receiver?

The quarterback uses proper throwing technique, including a tight grip on the football, a smooth arm motion, and a strong follow-through, to propel the ball towards the receiver.

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

The quarterback's footwork, arm strength, and throwing mechanics, as well as external factors such as weather conditions and the distance between the quarterback and receiver, can all impact the accuracy of the throw.

## 3. How does the receiver catch the football?

The receiver must use their hands to secure the football, typically by forming a "diamond" shape with their fingers and thumbs and bringing their hands together to catch the ball. They must also maintain focus and concentration to track the ball and make the catch.

## 4. What strategies can quarterbacks use to successfully complete a pass to a stationary receiver?

Quarterbacks can use a variety of strategies, such as reading the defense, adjusting their throwing velocity and trajectory, and communicating with their receiver through hand signals or verbal cues, to successfully complete a pass to a stationary receiver.

## 5. Why is it important for a quarterback to have a good connection with their receiver?

A strong connection between a quarterback and receiver is crucial for a successful pass. It allows them to anticipate each other's movements and make split-second decisions, leading to more accurate and efficient passes. This connection is often developed through practice and trust between the two players.

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