A particle is projected at an angle to the horizontal from a point on a smooth horizontal floor. It is found that ratio of the first maximum height attained to maximum height reached by it after 3rd c

Question

A particle is projected at an angle to the horizontal from a point on a smooth horizontal floor. It is found that ratio of the first maximum height attained to maximum height reached by it after 3rd collision with the floor is 2 36 1 0 12 ​ . Find coefficient of restitution between particle and floor.

TestHub · Accepted Answer

Each impact multiplies the vertical speed by e, so the maximum height multiplies by $e^{2}$ . After the 3rd collision: $\frac{H _{1}}{H _{3}} = e^{- 6} = \frac{1 0 ^{12}}{2 ^{36}}$ .

$e^{6} = \frac{2 ^{36}}{1 0 ^{12}} = (\frac{64}{100})^{6} \Rightarrow e = 0.64.$

Answer: (B)

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