# Ask an Expert: Banking a basket experiment

**Moderators:** kgudger, bfinio, MadelineB, Moderators

### Banking a basket experiment

Hello!

I am doing the banking your basket experiment for my sceience fair. I am computing the contact line lengths using algebra and geometry as well as have created the scaled down model to triangulate my findings.

I am struggling with computing X1 when Beta = 90 and the ball lands to the left and to the right. I know that when the ball lands center, Xtot = 0 and so X1 and X2 are both 0. However, when the ball lands right, I believe that Xtot = 0.11m with X1 = 0.01m and X2 = 0.10m. I believe that the numbers will remain the same for when the call lands left. But, then I run into the issue of having the length of my contact line for beta = 90 come out to be 0. This is obviously wrong. What am I doing wrong here? Also, as an FYI, I get contact line lengths of 0.04m at beta = 30, 0.07m at beta = 10, 0.02 at beta = 60. I hope those are correct. Any help is much appreciated. Thank you.

[Administrator note - https://www.sciencebuddies.org/science- ... #procedure ]

I am doing the banking your basket experiment for my sceience fair. I am computing the contact line lengths using algebra and geometry as well as have created the scaled down model to triangulate my findings.

I am struggling with computing X1 when Beta = 90 and the ball lands to the left and to the right. I know that when the ball lands center, Xtot = 0 and so X1 and X2 are both 0. However, when the ball lands right, I believe that Xtot = 0.11m with X1 = 0.01m and X2 = 0.10m. I believe that the numbers will remain the same for when the call lands left. But, then I run into the issue of having the length of my contact line for beta = 90 come out to be 0. This is obviously wrong. What am I doing wrong here? Also, as an FYI, I get contact line lengths of 0.04m at beta = 30, 0.07m at beta = 10, 0.02 at beta = 60. I hope those are correct. Any help is much appreciated. Thank you.

[Administrator note - https://www.sciencebuddies.org/science- ... #procedure ]

### Re: Banking a basket experiment

Hello! I see that an admin has attached the procedure as a note response. I have gone through the procedure several times in the past two weeks to no avail. I am still unable to determine how to calculate Xtot, X1 and X2 when the ball lands left/right when the player is at a 90 degree angle. Any hints or guidance will be much appreciated. Thank you. I’m happy to attach examples of my calculations so far.

### Re: Banking a basket experiment

Hi,

This project is outside of my expertise - it's been a long time since I worked through a geometry problem like this one! But I will try to help. And perhaps you'll get a much better response from your post in the Math and Computer Science forum.

First, I agree with you that the land left/right numbers are the same for the beta = 90 case.

Based on figures 8 and 9 (project procedure) I would say that the X dimensions are defined as follows:

Xtot is the distance along the plane of the backboard from the player position to the basket centerline;

X2 is the distance from the player position to the point where the ball contacts the backboard; and,

X1 is the distance from the point of ball contact to the centerline of the basket.

For the case of beta = 90, the player is aligned with the centerline of the basket. Based on the above definition Xtot must be zero. Since Xtot = X1 + X2 then X1 = -X2.

From figure 11 (project procedure) it appears that X1 should be a little less than the radius of the ball (0.109 m). Of course the value of X1 depends on the angle of incidence that you calculated.

I hope this helps. Please ask again if you have more questions.

A. Norman

This project is outside of my expertise - it's been a long time since I worked through a geometry problem like this one! But I will try to help. And perhaps you'll get a much better response from your post in the Math and Computer Science forum.

First, I agree with you that the land left/right numbers are the same for the beta = 90 case.

Based on figures 8 and 9 (project procedure) I would say that the X dimensions are defined as follows:

Xtot is the distance along the plane of the backboard from the player position to the basket centerline;

X2 is the distance from the player position to the point where the ball contacts the backboard; and,

X1 is the distance from the point of ball contact to the centerline of the basket.

For the case of beta = 90, the player is aligned with the centerline of the basket. Based on the above definition Xtot must be zero. Since Xtot = X1 + X2 then X1 = -X2.

From figure 11 (project procedure) it appears that X1 should be a little less than the radius of the ball (0.109 m). Of course the value of X1 depends on the angle of incidence that you calculated.

I hope this helps. Please ask again if you have more questions.

A. Norman

### Re: Banking a basket experiment

Thank you for the help and for pointing out that I inadvertently posted to Physical Sci instead of Math and CS. I will re-post. I will mull on your comments and revert back if more questions arise. Thank you again.