Establish the limitation which the uncertainty principle places on the precision with which the angle leaving the first pin may be set. Assuming that the uncertainties in the first collision are small, show that the uncertainty in the direction leaving the first pin is on the order of
where p=mv is the magnitude of the momentum the Pin Ball. From
this and the HUP, determine the least possible uncertainty
in the angle 
leaving pin #1.
(Note that the figure shows an exaggerated case where the
uncertainties 
and 
result is a rather
large uncertainty 
.)