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Newton's Laws for System of Particles

A ball hits t...

Question

A ball hits the ground and loses 20% of its momentum. Coefficient of restitution is (1) 0.2 (2) 0.4 (3) 0.6 (4) 0.8

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\frac{1}{\sqrt{0. ¯ ¯ ¯ 2} + \sqrt{0. ¯ ¯ ¯ 4}} + \frac{1}{\sqrt{0. ¯ ¯ ¯ 4} + \sqrt{0. ¯ ¯ ¯ 6}} + \frac{1}{\sqrt{0. ¯ ¯ ¯ 6} + \sqrt{0. ¯ ¯ ¯ 8}} + \frac{1}{\sqrt{0. ¯ ¯¯¯ ¯ 10} + \sqrt{0. ¯ ¯¯¯ ¯ 12}} + \frac{1}{\sqrt{0. ¯ ¯¯¯ ¯ 12} + \sqrt{0. ¯ ¯¯¯ ¯ 14}} + \frac{1}{\sqrt{0. ¯ ¯¯¯ ¯ 14} + \sqrt{0. ¯ ¯¯¯ ¯ 16}} + \frac{1}{\sqrt{0. ¯ ¯¯¯ ¯ 16} + \sqrt{0. ¯ ¯¯¯ ¯ 18}} + . . . . . .

. . . . . . . . . . . . . . . + \frac{1}{\sqrt{0. ¯ ¯¯¯ ¯ 38} + \sqrt{0. ¯ ¯¯¯ ¯ 40}} = \frac{3}{2} (\sqrt{a} + \sqrt{b}),

\frac{1}{\sqrt{0. ¯ ¯ ¯ 2} + \sqrt{0. ¯ ¯ ¯ 4}} + \frac{1}{\sqrt{0. ¯ ¯ ¯ 4} + \sqrt{0. ¯ ¯ ¯ 6}} + \frac{1}{\sqrt{0. ¯ ¯ ¯ 6} + \sqrt{0. ¯ ¯ ¯ 8}} + \frac{1}{\sqrt{0. ¯ ¯¯¯ ¯ 10} + \sqrt{0. ¯ ¯¯¯ ¯ 12}} + \frac{1}{\sqrt{0. ¯ ¯¯¯ ¯ 12} + \sqrt{0. ¯ ¯¯¯ ¯ 14}} + \frac{1}{\sqrt{0. ¯ ¯¯¯ ¯ 14} + \sqrt{0. ¯ ¯¯¯ ¯ 16}} + \frac{1}{\sqrt{0. ¯ ¯¯¯ ¯ 16} + \sqrt{0. ¯ ¯¯¯ ¯ 18}} + . . . . . .

. . . . . . . . . . . . . . . + \frac{1}{\sqrt{0. ¯ ¯¯¯ ¯ 38} + \sqrt{0. ¯ ¯¯¯ ¯ 40}} = \frac{3}{2} (\sqrt{a} + \sqrt{b}),

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