The juggler throws n balls per second. ∴ Interval between balls =
1
n
seconds
At maximum height velocity of first ball v=0 Juggler throws all balls with same initial velocity =u For 1 st ball, u1=u,v1=0,a=−g,S=Hmax Using formula, v2=u2+2as 0=u2−2gHmax ⇒Hmax=
u2
2g
...... (1) And using formula, v=u+at ⇒0=u−gt ⇒t=
u
g
∴ Time taken by ball 1 to reach maximum height (Hmax)=
u
g
According to the question, t=
1
n
⇒
u
g
=
1
n
⇒u=
g
n
......(2) Putting value of u in equation (1), we get Hmax=