# Projectile Motion of football receiver

• emilytm
In summary, the problem involves a football receiver running straight downfield at a constant speed, while the quarterback throws a pass at an angle above the horizon. The goal is to find the initial velocity of the football, the time it spends in the air, and the distance between the quarterback and receiver when the catch is made. The equations used involve the horizontal and vertical components of velocity, as well as the acceleration due to gravity. The time to reach maximum height is half of the total flight time, which can be found using the equation t=2Vo*sin theta/a. However, it is not possible to obtain Vo using this method and further assistance may be necessary.
emilytm

## Homework Statement

A football receiver running straight downfield at 5.5m/s is 10m in front of the quarterback when a pass is thrown downfield at 25 degrees above the horizon. If the receiver never changes speed and the ball is caught at the same height from which it was thrown find initial velocity of the football, the amount of time it spends in the air, and the distance between the quarterback and receiver when the catch is made.

## The Attempt at a Solution

I drew a diagram, found Vx=Vo*cos theta and Vy=Vo*sin theta. I also came up with the equations t=Vo*sin theta/ 9.81m/s^2 and t/2=delta x/ Vo*cos theta. Am I on the right track?

emilytm said:
I drew a diagram
Good
I found Vx=Vo*cos theta and Vy=Vo*sin theta.
OK [Edit: As @berkeman points out below, the second equation is only correct if Vy represent the y component of initial velocity, V0y.]
I also came up with the equations t=Vo*sin theta/ 9.81m/s^2
What time does this represent? Can you explain how you arrived at this expression?

Last edited:
emilytm
emilytm said:

## Homework Statement

A football receiver running straight downfield at 5.5m/s is 10m in front of the quarterback when a pass is thrown downfield at 25 degrees above the horizon. If the receiver never changes speed and the ball is caught at the same height from which it was thrown find initial velocity of the football, the amount of time it spends in the air, and the distance between the quarterback and receiver when the catch is made.

## The Attempt at a Solution

I drew a diagram, found Vx=Vo*cos theta and Vy=Vo*sin theta. I also came up with the equations t=Vo*sin theta/ 9.81m/s^2 and t/2=delta x/ Vo*cos theta. Am I on the right track?
Welcome to the PF.

Can you post how you came up with the last parts? Vy=Vo*sin theta is not right because the vertical velocity as a function of time depends on the acceleration of gravity.

On my initial sketch, I've assumed no air resistance, so the angle of the ball being caught matches the launch angle. The y height matches the initial thrown height (that gives an equation in y), and the equation in x involves the speed and initial position of the receiver. Can you post those equations as part of your work?

emilytm
berkeman said:
Vy=Vo*sin theta is not right
Oh, you probably meant to write Vyo=Vo*sin theta, not Vy(t) =Vo*sin theta. It's important to write the equations for x(t) and Vy(t) and y(t) as part of your solution...

emilytm
TSny said:
Good
OK [Edit: As @berkeman points out below, the second equation is only correct if Vy represent the y component of initial velocity, V0y.]
What time does this represent? Can you explain how you arrived at this expression?

It represented the time when the football was at maximum height.
TSny said:
Good
OK [Edit: As @berkeman points out below, the second equation is only correct if Vy represent the y component of initial velocity, V0y.]
What time does this represent? Can you explain how you arrived at this expression?

Yes I did mean to write Vyo.
I found time from the equation: delta x=Vo*cos theta*t.

For the first equation for time, I used Vy=Vyo+ay*t at Vy=0 and Vyo=Vo*sin theta (time at max height which is half the total time).

For the second equation, I used delta x=Vo*cos theta*t for total time.

emilytm said:
For the first equation for time, I used Vy=Vyo+ay*t at Vy=0 and Vyo=Vo*sin theta (time at max height which is half the total time).
OK, good.

For the second equation, I used delta x=Vo*cos theta*t for total time.
OK, but I'm a little confused with your notation in your first post. You used the symbol t for the time to reach maximum height. Then it looks like you used t/2 for the time in the Δx equation. That is, it looks like you used half the time to reach maximum height for the time in the Δx equation.

TSny said:
OK, good.

OK, but I'm a little confused with your notation in your first post. You used the symbol t for the time to reach maximum height. Then it looks like you used t/2 for the time in the Δx equation. That is, it looks like you used half the time to reach maximum height for the time in the Δx equation.

Oh, I see what you mean. It should have been just t in the delta x equation and t/2 in the other equation, t representing total time.

emilytm said:
Okay, I think I figured it out. I plugged in t=2Vo*sin theta/a into the equation delta y=Vyo*t+(1/2)at^2 and I got Vo=11.6 and t=2.37s.
I don't think it's possible to obtain Vo this way. Can you show more details of your calculation?

I do agree that the total flight time of the football is 2Vo*sin θ/|a|, where |a| is the magnitude of the acceleration.

If you want to use symbols such as θ, just click on the Σ symbol on the tool bar at the top of the window for entering your post.

This toolbar also has superscript and subscript icons, as well as other features.

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I forgot to square t. I think I am just going to get in person help on this. Thank you for your help!

## 1. What is projectile motion?

Projectile motion is the motion of an object through the air under the influence of gravity. In the case of a football receiver, the object is the football and the motion is the path it takes as it is thrown towards the receiver.

## 2. How does projectile motion affect a football receiver?

Projectile motion can affect a football receiver in terms of the trajectory and speed of the football. The receiver must be able to predict the path of the football in order to catch it, and must also be able to adjust their own motion to be in the right position to catch the ball.

## 3. What factors influence the projectile motion of a football receiver?

The factors that influence projectile motion of a football receiver include the initial velocity of the football, the angle at which it is thrown, the mass and shape of the football, air resistance, and the force of gravity.

## 4. How can a football receiver improve their ability to catch a ball in projectile motion?

A football receiver can improve their ability to catch a ball in projectile motion by practicing hand-eye coordination and reaction time, understanding the physics of projectile motion, and developing a strong understanding of their own abilities and limitations.

## 5. Can technology be used to analyze the projectile motion of a football receiver?

Yes, technology such as high-speed cameras and motion tracking software can be used to analyze the projectile motion of a football receiver. This can help coaches and players understand the mechanics of their movements and make improvements to their technique.

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