Football Vector Motion Problem

In summary, a quarterback running at a constant speed of 2.5m/s needs to throw a football at an angle relative to the sidelines in order to hit a stationary receiver straight downfield. Using the Pythagorean theorem and SOH CAH TOA, the quarterback can calculate the angle and the distance downfield of the receiver.
  • #1
Natko
44
0

Homework Statement


A quarterback is running across the field, parallel to the line of scrimmage, at a constant speed of 2.5m/s, when he spots an open, stationary receiver straight downfield from him (ie, in a line parallel to the sidelines). If he can throw the football at a speed of 8.0m/s, relative to himself, at what angle, relative to the sidelines, must he throw it in order to hit the receiver? How far downfield was the receiver?


Homework Equations


Pythagorean theorem
SOH CAH TOA


The Attempt at a Solution


IMG_0282.jpg
 
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  • #2
Your diagram performs the vector sum of two velocities at right angles. You sum two velocity vectors if one of them represents a velocity relative to the other. But the relative velocity is not given here - it's the thing you are trying to find.
See if you can get the right diagram.
 
  • #3
Does this look better?
IMG_0288.jpg

Sorry, it's flipped on PF even though I rotated it on my computer.
 
  • #4
Natko said:
Does this look better?
Yes, except that the arrow on the 8m/s goes the wrong way. When adding vectors diagrammatically, the contributing vectors connect nose-to-tail; the resultant runs from the tail of the first to the nose of the last.
 
  • #5

To solve this problem, we can use the Pythagorean theorem and the concept of vector motion. Since the quarterback is running parallel to the line of scrimmage, his velocity can be represented as a vector with a magnitude of 2.5m/s and a direction parallel to the sidelines. The receiver, being stationary, has a velocity of 0m/s.

We can also represent the throw as a vector with a magnitude of 8.0m/s and an unknown direction, which we will call θ. Using the concept of vector addition, we can add the velocities of the quarterback and the throw to find the overall velocity of the football. This can be represented by the formula Vf = Vq + Vt, where Vf is the final velocity of the football, Vq is the velocity of the quarterback, and Vt is the velocity of the throw.

Using this formula, we can break down the velocities into their x and y components. The x component of the football's velocity will be 8.0m/scosθ, and the y component will be 8.0m/ssinθ. The x component of the quarterback's velocity will be 2.5m/s, and the y component will be 0m/s.

Since the final velocity of the football must be equal to the velocity of the receiver (0m/s), we can set the x and y components of the final velocity equal to the x and y components of the receiver's velocity. This gives us two equations: 8.0m/scosθ = 0m/s and 8.0m/ssinθ = 0m/s.

Solving for θ, we get θ = 90°, meaning that the throw must be made at a 90° angle relative to the sidelines. To find the distance downfield the receiver is, we can use the formula d = vt, where d is the distance, v is the velocity, and t is the time. Since the receiver is stationary, t = 0. Therefore, the distance downfield is also 0m.

In conclusion, the quarterback must throw the football at a 90° angle relative to the sidelines in order to hit the receiver, who is 0m downfield.
 

1. What is a "Football Vector Motion Problem"?

A "Football Vector Motion Problem" is a physics problem that involves analyzing the motion of a football in terms of its direction and speed, also known as its vector components. This type of problem is commonly encountered in sports science and engineering.

2. How do you solve a "Football Vector Motion Problem"?

To solve a "Football Vector Motion Problem", you first need to identify the given information, such as the initial velocity, angle of the kick, and time of flight. Then, you can use equations from projectile motion to calculate the final velocity, distance traveled, and other relevant parameters.

3. What are some real-world applications of "Football Vector Motion Problems"?

"Football Vector Motion Problems" have many real-world applications, such as predicting the trajectory of a football during a game, designing more accurate and efficient footballs, and analyzing the performance of players in terms of their kicking abilities.

4. What types of equations are used to solve "Football Vector Motion Problems"?

The equations used to solve "Football Vector Motion Problems" are based on the principles of projectile motion, which include the equations for displacement, velocity, and acceleration in the x and y directions. These equations can also be modified to account for factors such as air resistance and spin on the football.

5. How can "Football Vector Motion Problems" be used to improve performance in football?

By analyzing and solving "Football Vector Motion Problems", coaches and players can gain a better understanding of the mechanics of kicking a football and make adjustments to improve their performance. This can also lead to the development of new training methods and equipment to enhance the overall performance of football players.

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