What is the required velocity to make the field goal?

In summary, the problem involves finding the distance and height of a ball launched at a 45 degree angle towards a field goal. The equations provided are necessary for solving the problem. The key is to recognize that the horizontal velocity is constant, while the vertical velocity is affected by gravity. The initial horizontal and vertical components of the velocity can be found using the given information.
  • #1
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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  • #2
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:
 
  • #3
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?
 

FAQ: What is the required velocity to make the field goal?

What is the required velocity to make the field goal?

The required velocity to make a field goal depends on a few different factors, such as the distance from the goalposts and the angle at which the ball is kicked. However, on average, a field goal requires a velocity of around 50-60 miles per hour.

Can the required velocity for a field goal vary?

Yes, the required velocity for a field goal can vary depending on the specific circumstances of the kick. For example, a longer distance or a more difficult angle may require a higher velocity. Additionally, environmental factors such as wind can also affect the required velocity.

How do you calculate the required velocity for a field goal?

The required velocity for a field goal can be calculated using the equation v = square root of (g * d / sin(2 * theta)), where v is the velocity, g is the acceleration due to gravity (9.8 m/s^2), d is the distance from the goalposts, and theta is the angle at which the ball is kicked.

Does the weight of the ball affect the required velocity for a field goal?

Yes, the weight of the ball can affect the required velocity for a field goal. A heavier ball will require a higher velocity to reach the same distance as a lighter ball, while a lighter ball will require less velocity. However, the weight of the ball is typically standardized for football games, so this may not have a significant impact on the required velocity in most cases.

Is there an optimal velocity for making a field goal?

Yes, there is an optimal velocity for making a field goal. This can vary depending on the specific circumstances of the kick, but in general, a velocity of around 55 miles per hour is considered to be ideal for making a field goal.

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