A ball kept at $20 \mathrm{~m}$ height falls freely in downward direction vertically and hits the ground.…

A ball kept at $20 \mathrm{~m}$ height falls freely in downward direction vertically and hits the ground. The coefficient of restitution is $0.4 .$ After the first rebound the upward velocity is $\left[\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right]$
  1. $8 \mathrm{~m} / \mathrm{s}$
  2. $12 \mathrm{~m} / \mathrm{s}$
  3. $4 \mathrm{~m} / \mathrm{s}$
  4. $16 \mathrm{~m} / \mathrm{s}$

Solution

$8 \mathrm{~m} / \mathrm{s}$ $h=20 \mathrm{~m}, \mathrm{e}=0.4 \mathrm{~m}$ $\therefore v^{2}=0+2 g h=2 \times 10 \times 20$ $\therefore v=2 \times 10=20$ $e=\frac{\mathrm{u}}{\mathrm{v}}$ $\therefore \mathrm{u}=\mathrm{ev}=0.4 \times 20=8 \mathrm{~m} / \mathrm{s}$

Asked in: MHT CET 2020 (20 Oct Shift 1)

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