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Can you pre-determine the result of a coin toss?

$ \begingroup $ At the very least you would besides need the dimensions of the mint ( mass alone is not enough ) and the elastic properties of both the coin and of the come on on which you land … that has a big impingement ( since the coin can bounce or “ stick ”, depending on the surface ). It may be possible to predict for certain sizes of coin and altitude of drop ( a cautiously executed half-flip of a huge coin ) – but as the numeral of revolutions completed increases, and particularly if the count position at the time of landing approaches the metastable position ( landing on edge in such a way that it is equally probable to fall to either side ) the uncertainty in the result besides increases, until you end up with a resounding “ no ” .
In general, then, the answer is “ no ”. For specific cases the answer can be “ yes ”. It all depends …
But if I were asked to do the calculation – which was your wonder – I would good solve the equations of gesture. Assuming that you have the take after information

m = mass of coin
I = moment of inertia about length axis
g = acceleration of gravity
h = initial height
d = distance from center of mass where impulse is applied
p = impulse applied to coin

you can then compute the initial vertical speed from
$ $ v = \frac { p } { thousand } $ $

and therefore the time to land by beginning computing the maximum altitude ( which will be reached after $ t=v/g $ seconds, and be at $ h_ { soap } =h+\frac12 g t^2 $ ), and then the clock time from this acme to the ground, given by $ t_2=\sqrt { 2 h_ { soap } /g } $. You would credibly want the time until you reach “ prime minus radius of coin ” so you can compute the clock when you actually strike the surface – this depends on the angular situation of the coin .
Next you would compute the angular speed of the coin from

$ $ \omega = \frac { p d } { I } $ $
With these two numbers you can calculate how many revolutions the coin has completed when it gets close to the grind, and then you would have to figure out when the coin first hits the surface – this is not when the center of aggregate hits h=0, but rather when a rim of the coin does – and that depends on the angular position .
last, you would have to take into history the properties of the surface to determine how the mint behaves when it hits the ground. This can be the trickiest function of the calculation – which is why I started out by saying that the surface properties absolutely need to be separate of the input signal .

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Category : Economy

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