How to calculate the speed of the ball at the moment of crossing the laser beam?

Question

Circuit design

I am making a project on Arduino, and now I needed to find out how fast the ball rolls through the laser beam.

Can anyone help?
Given:
* Ball (with a constant diameter d)
* Line crossing detent: laser diode + photoresistor (that is, we know the time for which the laser was interrupted when crossing)
Find:
The speed of the ball (ms / s)
Suggest a formula or at least where look.
UPD: Yes, of course, the problem is that the ball can both fly up and edge along the beam.

Answer 1

In theory, it is possible with one sensor - a Doppler meter.
https://ru.wikipedia.org/wiki/%D0%94%D0%BE%D0%BF%D...
As an example:
www.lib.tpu.ru/fulltext/c/2012/C18/029. pdf
In practice, this is probably quite expensive.

Answer 2

Is the ball rolling on a plane? In this case, if you set the system at a height equal to the radius, the ball cannot hit the beam with an edge. The problem will be that it can pass at an angle to the beam, and the light will be interrupted for a time greater than d/v. It will be necessary to put two beams at an angle to each other. The easiest way is if they are perpendicular - then the speed will be determined as d*sqrt(1/t1^2+1/t2^2). If a right angle is not possible, then two answers will be obtained - one when the direction of the ball falls into a large angle between the rays, and the second - when it enters a small angle.
If the ball flies in space, then the chances that it will cross the beam at all are very small. But if we assume that this happens, then we will have to take several parallel beams (for example, three, forming a strip, with a small distance between them), and by the ratio of the time that the ball crosses them, determine in what place it hit them. Although no, three is not enough. After all, the ball can also fly up parallel to the plane of this strip, then all sensors will show the same time. It is better to take 5 rays that form a cross (the vertices of the square and the center).
And 5 more rays going at an angle to the first to compensate for the angle at which the rays intersect with the ball. A total of 10 - and the system will work only if the ball crosses them all.

Answer 3

If the beam passes through the center of the ball, then you just need to divide the diameter d by the time the beam is interrupted. Is this simple, or am I missing something?