A juggler keeps (n) balls going with one hand so that at any instant, ( n-1) blls in air in air and one ball in the hand, If each ball rises to a height of 9x) metre, find the time for which each ball stays the hand.

Explanation

Let (u) the linitial velocity of the ball while goig upwards. The final velocity of the ball at height (x) is,
` v=0`.
Using the relation , ` v^2 = u ^2 = 2 a S, we have ` o= u^2 - 2 gx ` or ` u =sqrt 2 gx`
If (t) is the time taken by ball in going up through distance` (x), when ` 0= u + ( - g0 t ` or t = u/g`.
Total time after which the ball comes into the hand is , ` T= 2 t = ( 2u0/ g 2/g sqrt( 2 gt) = 2 sqrt ( 2x)/g`
During time (T), (n- 1) balls will be in air and ne ball will be in hand.
Time for one ball in hand `= T/(n-1) = ( 2 aqrt 2 x //g)/ (( n-1)) = 2/( ( n-1)) sqrt ( 2x)/g`.