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 metre, then the value of n is ___________.

If they meet at t=t0. ∴ h−55=12gt0−22  (for ball B)      .........(i)where, h is height of the building. The velocity of each ball at the meeting point is v0.∴ v0=gt0−2Let the time taken by ball A to go from meeting point ground is t1∴ t0=t0−2+2t1 Or t1=1s∴ 55=v0t1+12gt12 Or  55=gt0−2t1+12gt12 Or  5.5=t0−2t1+t122=t0−2+12 Or  5=t0−2∴    t0=7s∵     h−55=12gt0−22 Or     h−55=5(7−2)2=125∴     h=55+125=180m=60 nm∴     n=3