What is the required velocity to make the field goal?

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SUMMARY

The discussion focuses on calculating the required initial velocity for a projectile (a football) to successfully clear a field goal from a distance of 50 meters at a height of 4 meters, launched at a 45° angle. The relevant equations of motion provided include Vfx = Vix + ax * t and Vfy = Viy + ay * t^2. Participants emphasize the importance of recognizing that horizontal velocity remains constant while vertical velocity is influenced by gravitational acceleration (9.8 m/s²). The goal is to derive the initial velocity needed to achieve the desired trajectory.

PREREQUISITES
  • Understanding of projectile motion principles
  • Familiarity with kinematic equations
  • Knowledge of vector components of velocity
  • Basic grasp of gravitational acceleration (9.8 m/s²)
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  • Learn how to resolve velocity into horizontal and vertical components
  • Practice solving similar projectile motion problems with varying angles and distances
  • Explore the effects of air resistance on projectile trajectories
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Students studying physics, particularly those focusing on mechanics and projectile motion, as well as educators seeking to enhance their teaching methods in kinematics.

sololight
(First homework post I've ever made, I encourage you to tell me if I typed something that does not follow policy.)

1. Homework Statement

Distance on the X axis from the ball's location to the field goal = 50 m
Height on the Y axis of the field goals height = 4 m
Ball's angle = 45° θ

Homework Equations



Vfx = Vix + ax * t
Vfy = Viy + ay * t^2

Xf = Xi + Vix * t + 1/2 * a * t^2
Yf = Yi + Viy * t + 1/2 * a * t^2

These were provided by the teacher, he told me these were the equations that you needed to solve.

The Attempt at a Solution



I feel like I am completely missing the point to this problem. The equations look like a huge mess to me, I am struggling to figure out which equation I must use first, my attempt was pitiful and it got nowhere but here it is:

First I just try to solve an equation that comes to mind, for instance, Vfx. Couldn't we assume that the initial velocity of x is 0? I don't know the acceleration of x nor time. So I get: Vfx = 0 + ax * t

The same goes with Vfy, I get Vfy = 0 + ax * t.

For Xf, I assume that the initial X position is 0, the initial velocity of x is 0, I don't know the time but acceleration is 9.8. I end up with 0 + 0 + 4.9 * t^2.

I get the same thing for Yf aswell.

I am clearly missing the point of this problem, I need to find all the unknowns. Perhaps I am not using enough or maybe even the correct equations. I would like to find out the time, when to use the 9.8 m/s as acceleration, and of course the answer to the original problem. All of this has been very frustrating, yet, fun at the same time. I appreciate any help.
 
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Welcome to the PF. :smile:

In these types of projectile motion problems, recognize that (without air resistance) the horizontal velocity is constant throughout the flight. The vertical velocity is affected by the downward acceleration of gravity.

So write the equation for the horizontal position of the ball versus time. Them write the equation for the vertical position versus time. Then fill in the final x,y values of the position of the ball as it barely clears the crossbar. Then solve the equations!

Give that a try and show your work. Thanks. :smile:
 
sololight said:
Couldn't we assume that the initial velocity of x is 0?
You are not given an initial speed, just the launch angle. The aim is to find that speed.
If the initial speed is u and the launch angle is 45 degrees, what are the initial horizontal and vertical components of that velocity?
 

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