$2\mathrm{.}3(*$Dribbling basket balls$).$ Identify a requirement on the initial state of the bouncing ball that allows it to move initially, so is more general than $v=0.$

Prove that this variation of the bouncing ball is safe.

Hint: This requires to handle the case with initial velocity v You may try to find a precondition among the initial height H$,$ the initial velocity v$,$ and the damping coefficient c$.$