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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. |
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Answer» 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`. |
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