A juggler throws balls almost vertically upwards, with time $\backslash$Delta t $=0\mathrm{.}23$ s $\backslash$Delta t$=0\mathrm{.}23$ s between each throw. $($Yes$,$ pretty amazing.$)$ The balls are all thrown to the same height, and in repeated succession $($e$.$g$.1,2,3,1,2,3$ etc.$).$ Let's simplify: neglect air resistance, neglect the time between catching and throwing a ball and assume that balls are thrown and caught at the same height. Calculate the minimum height he must throw the balls if he is to juggle $3$ balls? $\_\_\_\_\_$ m m