Balls A and B are released from rest from roof of a building at t=0 and t=2 s, respectively. The ball A strikes with ground and comes back with same speed. After some time, both balls A and B meet with each other at a height of 55 m from the ground. If the height of building is 60n meter, then the value of n is _______

If they meet at t=t0 .  t0 is the total time taken by ball A  from P to Q and Q to R (t0-2) is the total time taken by ball B  from P to RBall B: P to R ∴ h−55=12gt0−22  (for ball B )    ......(i)where, h is height of the building. Let say the velocity of each ball at the meeting point is v0.∴ v0=gt0−2----(ii)     for ball BLet the time taken by ball A to go from meeting point to ground is t1.total time taken by A=time taken from P to R +time taken from R to Q +time taken from Q to R t0=(t0-2)+t1+t12=2t1t1=1s---(iii) R to Q: ∴ 55=v0t1+12gt12or 55=gt0−2t1+12gt12or 5.5=t0−2t1+t122=t0−2+12or 5=t0−2∴    t0=7s Substitute in (i)∵     h−55=12gt0−22 Or     h−55=5(7−2)2=125∴    h=55+125=180m=60n∴    n=3