What Part of a Ball Hitting a Parabola Hits the Focal Point?

In summary, the discussion is about a 1" ball hitting the inside of a parabola and whether the edge or center of the ball would hit the focal point. There is no exact answer as it depends on the ball's trajectory and the parabola's shape. Under certain conditions, the ball can hit the focal point with its side. However, for a ball flying parallel to the axis, the only possible solutions are from the center to the side.
  • #1
Photon713
19
0
1" ball hitting Parabola

If a 1" ball hits the inside of a parabola, what part of the ball hits the focal point?
Is it the edge that strikes the inside of the parabola or the center of the ball?
Thank You
 
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  • #2


What are your thoughts on the matter?
 
  • #3


I think it would be the outer edge of the ball.
 
  • #4


I modeled the problem using rhino geometry. Attached 1 pic with a ball crossing the focus.
There is no exact answer.

If the ball follows the parabola axis it will hit dead center (obvious).
But in all other situations, the ball might cross the focus or even miss it completely.
The ball can hit the focus with it's side given certain conditions.
 

Attachments

  • Paraball.jpg
    Paraball.jpg
    12.3 KB · Views: 454
  • #5


Lok said:
I modeled the problem using rhino geometry. Attached 1 pic with a ball crossing the focus.
There is no exact answer.

If the ball follows the parabola axis it will hit dead center (obvious).
But in all other situations, the ball might cross the focus or even miss it completely.
The ball can hit the focus with it's side given certain conditions.
Cool. But I don't see from your diagram under what circumstances it would miss the focus completely.
 
  • #6


Thank You...

I am attaching an image that represents a 1" ball bearing hitting the inside of a parabola.
Which line represents the passage through the focal point, center or edge? Is the result always the same no matter where the bearing hits the side?
 

Attachments

  • Parabola7.7x4.jpg
    Parabola7.7x4.jpg
    8.3 KB · Views: 466
  • #7


DaveC426913 said:
Cool. But I don't see from your diagram under what circumstances it would miss the focus completely.

For ball flying parallel to the axis there are only center to side solutions. But for different angles it is not true. The problem did not specify parallelism though.
 

Related to What Part of a Ball Hitting a Parabola Hits the Focal Point?

1. What is a parabola?

A parabola is a symmetrical curve that is formed by the intersection of a plane and a cone when the plane is parallel to one of the cone's sides. It is a common shape seen in mathematics and can be described by the quadratic equation y = ax^2 + bx + c.

2. How does a ball hitting a parabola relate to science?

When a ball is thrown or hit, it follows a parabolic path due to the forces of gravity and air resistance. This motion can be predicted and analyzed using principles of physics, making it a topic of interest in the field of science.

3. What factors affect the shape of a ball hitting a parabola?

The shape of the parabola formed by a ball hitting it is affected by several factors, including the initial velocity and angle of the ball, the mass and size of the ball, and the air resistance and gravity acting on the ball.

4. Can a ball hit a perfect parabola?

In theory, yes, a ball can hit a perfect parabola if it is thrown or hit with the perfect combination of initial velocity and angle. However, in reality, factors such as air resistance and the imperfections of the ball's movement can cause the shape of the parabola to deviate slightly from perfection.

5. How is the motion of a ball hitting a parabola used in real-life applications?

The principles of a ball hitting a parabola are used in various real-life applications, such as in sports like baseball and golf for predicting the trajectory of a ball. It is also used in engineering and physics to study projectile motion and design structures that can withstand the forces of a ball hitting a surface at different angles.

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