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A rubber ball is

Question:

A rubber ball is released from a height of $5 \mathrm{~m}$ above the floor. It bounces back repeatedly, always rising to $\frac{81}{100}$ of the height through which it falls. Find the average speed of the ball. (Take $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )

  1. $3.0 \mathrm{~ms}^{-1}$

  2. $3.50 \mathrm{~ms}^{-1}$

  3. $2.0 \mathrm{~ms}^{-1}$

  4. $2.50 \mathrm{~ms}^{-1}$


Correct Option: , 4

Solution:

(4) $v_{0}=\sqrt{2 g h}$

$\mathrm{v}=\mathrm{e} \sqrt{2 \mathrm{gh}}=\sqrt{2 \mathrm{gh}}$

$\Rightarrow \mathrm{e}=0.9$

$S=h+2 e^{2} h+2 e^{4} h+\ldots \ldots \ldots$

$\mathrm{t}=\sqrt{\frac{2 \mathrm{~h}}{\mathrm{~g}}}+2 \mathrm{e} \sqrt{\frac{2 \mathrm{~h}}{\mathrm{~g}}}+2 \mathrm{e}^{2} \sqrt{\frac{2 \mathrm{~h}}{\mathrm{~g}}}+\ldots \ldots \ldots$

$\mathrm{v}_{\mathrm{av}}=\frac{\mathrm{s}}{\mathrm{t}}=2.5 \mathrm{~m} / \mathrm{s}$

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