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

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

Solution

$\begin{aligned} v^2 & =0+2 g h \quad \ldots\left(\because v^2-u^2=2 g h\right) \\ & v^2=2 \times 10 \times 20=400 \\ & v=20 \mathrm{~m} / \mathrm{s} \\ & \mathrm{e}=\frac{\mathrm{u}}{\mathrm{v}} \end{aligned}$ $\therefore \quad$ The velocity of the body after the first rebound is $\begin{aligned} & u=0.4 \times 20 \\ & u=8 \mathrm{~m} / \mathrm{s} \end{aligned}$

Asked in: MHT CET 2023 (11 May Shift 2)

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