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 $$___________$$.

Question

Infinity Learn · Accepted Answer

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∴     $$n=3$$

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