Question

# Aball is droped from the top of the tower of height h .It covers a distance of h/2 in the last second of its motion .How long does the ball remain in air .(Take g = 10 ms−2)

A
2 s
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B
(2+2) s
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C
2s
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D
None of the above
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Solution

## The correct option is C (2+√2) sLet time during which ball remain in the air t,From the kinematics,s=ut+12gt2 (u=0m/s)h=gt22. . . . .(1)The distance travelled by the ball in nthsec is given bySn=u+g2(2n−1)at n=(t−1)sech2=g2[2(t−1)−1]h=g(2t−3). . . . . (2)By solving equation (1) and (2), we getgt22=g(2t−3)t2−4t+6=0 (Quadratic equation)t=√2√2−1By rationalisig,t=√2√2−1×√2+1√2+1t=(2+√2)sThe correct option is B.

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