Originally Posted by Camron Rust (Post 540504)

Below the red line, it is not possible for the ball to go into the basket without going over the backboard. Think of the red line as the path of the center of the ball. If the center of the ball is above that line, it can't go in....it will bounce out. If the center of the ball is below that line, it must go over the board (and may still miss).

Originally Posted by sseltser (Post 540716)

Camron

This is a sweet picture and pretty accurate for our purposes, but there is a slight error that I think you might want to think about.

Consider the area that is inside the ring, but to the "upper left" of the red line. Technically speaking, if the center of the ball happens to drop (straight down or nearly straight down) anywhere inside that area then the ball will bounce toward the center of the basket and have a chance to go in.

Therefore, to get the actual solution for the red line would require this (and I'm not proposing to do this because I've already taken Calc 1 and 2 and don't feel like repeating it):

- The red line would have to be tangent to the curve that is represented by the ring. Therefore, we need en equation of the half circle that is the "upper half" of the ring.
- We probably need to get a function of its derivative.
- Finally we need to find a line that has these three characteristics:
a)passes through the outside point of the backboard (as in the drawing)
b)passes through a point on the ring ( (x,f(x)) where f is the curve of the ring)
C)has the same slope as the instantaneous slope of the curve of the ring that it passes through.



Now that I've done that kind of work for the first time since my sophomore year, if anybody wants to actually figure it out (and find out that the real answer is like 8.6') then they have more free time on their hands than I do.

Originally Posted by sseltser (Post 540716)

Camron

This is a sweet picture and pretty accurate for our purposes, but there is a slight error that I think you might want to think about.

Consider the area that is inside the ring, but to the "upper left" of the red line. Technically speaking, if the center of the ball happens to drop (straight down or nearly straight down) anywhere inside that area then the ball will bounce toward the center of the basket and have a chance to go in.

Therefore, to get the actual solution for the red line would require this (and I'm not proposing to do this because I've already taken Calc 1 and 2 and don't feel like repeating it):

- The red line would have to be tangent to the curve that is represented by the ring. Therefore, we need en equation of the half circle that is the "upper half" of the ring.
- We probably need to get a function of its derivative.
- Finally we need to find a line that has these three characteristics:
a)passes through the outside point of the backboard (as in the drawing)
b)passes through a point on the ring ( (x,f(x)) where f is the curve of the ring)
C)has the same slope as the instantaneous slope of the curve of the ring that it passes through.



Now that I've done that kind of work for the first time since my sophomore year, if anybody wants to actually figure it out (and find out that the real answer is like 8.6') then they have more free time on their hands than I do.

Originally Posted by rainmaker (Post 540657)

Sheez, Camron, you have way, way too much time on your hands!!

Originally Posted by Ch1town (Post 540243)

I stand corrected. Had to go back & re-read the OP. This line got me: "passing directly behind the backboard".

Reading IS fundamental!

Originally Posted by btaylor64 (Post 540859)

If it reads as you stated that would mean it would be illegal for the ball to go through the supports. Does it really say that?

Originally Posted by mutantducky (Post 558223)

So to clarify because some things are getting jumbled

Originally Posted by MajorCord (Post 540186)

Player A is falling out of bounds under his own basket. He throws the ball behind his back in an effort to save the ball. In doing so, the ball goes from one side of the lane to the other, passing directly behind the backboard, and somehow comes down on the other side of the lane without hitting any supports where it is caught by a teammate. Officials had a "no call". A D-1 official observing said that the play should have been whistled. He says that the ball cannot pass directly behind the backboard. What say you guys and gals?