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Question

A stone falls freely from rest from a height h and it travels a distance 9h25 in the last second. The value of h is (Take g=10m/s2):

A
145m
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B
100m
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C
125m
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D
200m
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Solution

The correct option is C 125m

Step 1: Equations of motion for Last second
Let the total time of fall is 't' s, in the last second (tth second) displacement is 9h25
Initial speed u=0 ; Acceleration a=g

Using expression for displacement in nth second (Taking downward positive)
Sn=u+a2(2n1)
9h25=g2(2t1) ....(1)

Step 2: Equations of motion for whole motion
(Taking downward Positive)
s=ut+12at2
Putting s=h and u=0
h=12gt2 ....(2)

Step 3: Equation solving
From equation (1) and (2)
25g18=12gt2
9t250t+25
t=5s

From equation (2)
h=12×10×(5)2
=125m

Hence the value of h is 125 m.
Option C.

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