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  • A stone is dropped from a height of 80 m. If  , what is

A stone is dropped from a height of 80 m. If  g=10 \mathrm{~ms}^{-2}, what is the ratio of the distances travelled by it during the first and the last second of its motion?

Option: 1

\frac{1}{2}


Option: 2

\frac{1}{4}


Option: 3

\frac{1}{5}


Option: 4

\frac{1}{7}


Answers (1)

best_answer

Since the initial velocity of the stone is zero,

the total time taken by the stone to hit the ground is given by

h=\frac{1}{2} g t^2 \ or \ \ t=\sqrt{\frac{2 h}{g}}=\sqrt{\frac{2 \times 80}{10}}=4 \mathrm{~s}
During the first second, the stone falls a distance h_1  given by

h_1=\frac{1}{2} g(1)^2=\frac{g}{2}=5 \mathrm{~m}
During the first three seconds, the stone falls a distance h given by h=\frac{1}{2} g(3)^2=45 \mathrm{~m}
Therefore Distance h_2 through which the stone falls in the last (i.e. fourth) second =80-45=35 \mathrm{~m}.

Now h_1 / h_2=5 / 35=1 / 7. 

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