Question

A ball is thrown on downwards with initial speed$=6m/s$, from a point at height$=3.2m$ above a horizontal floor. If the ball rebounds back to the same height then coefficient of restitution equal to:

• A. $1/2$
• B. $0.75$
• C. $0.8$
• D. $None$

Answer 1

The correct option is C $0.8$

Final velocity v of the ball$=\sqrt{u^2+2gs}=\sqrt{36+2\times 10\times 3.2}=10m/s$

Now for the ball return flight after rebounding, since it just reaches height 3.2m final velocity=0

To reach height 3.2m initial velocity require $u=\sqrt{2\times 10\times 3.2}=8m/s$

Coefficiet of restitution:

$C_R=\sqrt{\frac{K.Eafterimpact}{K.Ebeforeimpact}}=\sqrt{\frac{\frac{1}{2}m{v}^2}{\frac{1}{2}m{u}^2}}=\sqrt{\frac{v^2}{u^2}}=\frac{v}{u}$

$C_R=\frac{8}{10}=0.8$