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Question

A body is dropped form the top of a tower. It falls through 40 m during the last two seconds of its fall.The height of tower in m is (g=10ms2)

A
45 m
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B
50 m
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C
60 m
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D
80 m
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Solution

The correct option is A 45 m
In the case of free fall displacement of the motion is
S=12gt2
let assume
nth second = tn
(n-2)th second = tn2
given that (tntn2)=2...(1)
Displacement in last two seconds,
S(n,n1)th=12g(tntn2)2
putting values in this equation
40=12×10×(tntn2)2
(tntn2)(tn+tn2)=8
(tn+tn2)=4...(2)
by solving eq 1 and eq 2 we get the values of
tn=3tn2=1
hight of the building
S=12gt2
S=12×10×32
S=45m

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