    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 125mStep 1: Equations of motion for Last secondLet the total time of fall is 't' s, in the last second (tth second) displacement is 9h25Initial speed u=0 ; Acceleration a=g Using expression for displacement in nth second (Taking downward positive) Sn=u+a2(2n−1) ∴9h25=g2(2t−1) ....(1)Step 2: Equations of motion for whole motion(Taking downward Positive) s=ut+12at2Putting s=h and u=0 ⇒ h=12gt2 ....(2)Step 3: Equation solvingFrom equation (1) and (2) 25g18=12gt2 9t2−50t+25 ⇒t=5sFrom equation (2) h=12×10×(5)2 =125mHence the value of h is 125 m.Option C.  Suggest Corrections  0      Similar questions  Related Videos   Motion Under Gravity
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