Question

a juggler throws ball up with equal speed he releases a ball when the previous one has reached half the maximum height the maximum number of balls moving in the upward direction at any one instant is?

Answer 1

the answer for this question is 4 plz solve for it

Answer 2

well here we go..
the basic idea is to find out if u throw a ball up & it takes time 't' then how much does it take to go half way..
so we proceed in a following manner..
we apply the following equation to find out the relation in between velocity with which the ball is thrown(V) and maximum height attained(h)
we have at the maximum height
\[0^{2}-V^{2}=-2*10*h\]
which means
h=(V^2)/20 or V=sqrt(20)h

now we calculate the velocity when ball is at height h/2 & going up we call it velocity V2..
apply the same equation by putting sqrt(20h) in the place of initial velocity & h/2 in place of h..
we have V2=sqrt(10h)

now we calculate the time taken to reach maximum height
t=0-sqrt(20h)/-10

calculate the time taken t2 to reach half way i.e..h/2
t2=(sqrt(10h)-sqrt(20h))/-10

divide the equation for time t by this above equation to get a relation betweeen t2 and t
as
\[t_{2}=(\sqrt{2}-1)t/\sqrt{2}\]

if u calculate it it is approximately 0.29 times the total time going up.. means ball takes only 0.29t time to go half way & 0.71t time to go another half means from h/2 to h & that is obvious if u think upon it ..

now we start calculation..
at time t=0 we throw 1st ball
this ball goes half way in time 0.29t
at time 0.29t you throw a 2nd ball..which reaches halfway in 0.58t
at time 0.58t you throw the third ball & remmber the 1st ball u launched is still moving up till the time t as we proved above..& at time 0.97t u throw the fourth ball

now you can see clearly that all four balls are still in air and moving up.. the very 1st ball u launched will reach maximum height at time t and will come down only after that..

think upon it and you will analyze that 4 is the maximum no. although you can have at a particular moment only three balls moving up but in maximum only three....