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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 m
If 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 (t1), thus we have
t1=  2(H2)g ......(ii)
Subtracting (i) from (ii), we get
2Hg  2(H2)g=1
Or Hg(21)=1
Or Hg=10.414
Or H=58.3 m
Total time of fall is t=2Hg=3.4 s

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