Question

# A body travels half of its total path in the last second of its fall from rest. If t and H are the time and height of its fall (take g=10 m/s2). Then,

A
t=2.4 s
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B
t=3.4 s
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C
H=28.8 m
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D
H=58.3 m
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Solution

## The correct option is D H=58.3 mIf H be the total height by which the body falls, then the total time to fall is given by H=ut+12gt2 As u=0 ⇒t=√2Hg .....(i) It is given that the body falls H2 distance in time (t−1), thus we have t−1=  ⎷2(H2)g ......(ii) Subtracting (i) from (ii), we get √2Hg−  ⎷2(H2)g=1 Or √Hg(√2−1)=1 Or √Hg=10.414 Or H=58.3 m Total time of fall is t=√2Hg=3.4 s

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