Kinematics Question 409

Question: A stone falls freely under gravity. It covers distances $ h _{1},h _{2} $ and $ h _{3} $ in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between $ h _{1},h _{2} $ and $ h _{3} $ it’s

Options:

A) $ h _{1}=\frac{h _{2}}{3}=\frac{h _{3}}{5} $

B) $ h _{2}=3h _{1}andh _{3}=3h _{2} $

C) $ h _{1}=h _{2}=h _{3} $

D) $ h _{1}=2h _{2}=3h _{3} $

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Answer:

Correct Answer: A

Solution:

$ \therefore h=\frac{1}{2}gt^{2}\text{ }\therefore {{h} _{1}}=\frac{1}{2}g{{( 5 )}^{2}}=125 $

$ {{h} _{1}}+{{h} _{2}}=\frac{1}{2}g{{( 10 )}^{2}}=500\Rightarrow {{h} _{2}}=375 $

$ \therefore {{h} _{1}}+{{h} _{2}}+h _{3}=\frac{1}{2}g{{( 15 )}^{2}}=1125 $

$ \Rightarrow h _{3}625 $

$ h _{2}=3h _{1},h _{3}=5h _{1}\text{ or }{{h} _{1}}=\frac{h _{2}}{3}=\frac{h _{3}}{5} $



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