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Q.

A series of n identical balls is shown on a smooth horizontal surface. If number 1 moves horizontally with speed u into number 2, which in turn collides with number 3 etc… and the coefficient of restitution for each impact is e, determine the speed of the nth ball

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a

$\frac{{(1 + e)}^{n - 1} u}{2^{n - 1}}$

b

$\frac{{(1 - e)}^{n} u}{2^{n}}$

c

$\frac{{(1 + e)}^{n} u}{2^{n}}$

d

$\frac{{(1 + e)}^{n + 1} u}{2^{n + 1}}$

answer is A.

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Detailed Solution

Series of n identical ball, ball 1 collides with ball 2 with u, e
Question Image
${mu=mv}_{1} {+mv}_{2} {eu=v}_{2} - v_{1} e = \frac{v_{2} - v_{1}}{u} (1 + e) \frac{u}{2} = v_{2} v_{3} = (1 + e) \frac{v_{2}}{2} = \frac{(1 + e)}{2} \frac{(1 + e) u}{2} = \frac{{(1 + e)}^{2}}{2^{2}} v_{n} = \frac{{(1 + e)}^{n - 1} u}{2^{n - 1}}$

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