Question

A small ball moving with a velocity $10\text{m/s}$, horizontally (as shown in figure) strikes a rough horizontal surface having $\mu =0.5$. If the coefficient of restitution is $e=0.4$. Horizontal component of velocity of the ball after $1^{\text{st}}$ impact will be $(g=10{\text{m/s}}^2)$

• A. $10\text{m/s}$
• B. $8\text{m/s}$
• C. $3\text{m/s}$
• D. $4\text{m/s}$

Answer 1

The correct option is C $3\text{m/s}$

Impulse due to Normal
$\int Ndt=m{v}_y-m{u}_y,e=\frac{v_y}{u_y}\Rightarrow v_y=0.4\times \sqrt{2g\left(5\right)}=0.4\times 10=4\text{m/s}$

$\int Ndt=m\times 4-(-10m)=14m$
Impulse due to friction
$-\int \mu Ndt=m{v}_x-m{u}_x$
$-0.5\times 14m=m{v}_x-m\times 10\Rightarrow v_x=3\text{m/s}$