Question

As shown in the figure, a body of mass $m$ moving vertically with speed $3m/s$ hits a smooth fixed inclined plane and rebounds with a velocity $v_f$ in the horizontal direction. If the angle of inclination is ${30}^{\circ }$, the velocity $v_f$ will be

• A. $3m/s$
• B. $\sqrt{3}m/s$
• C. $1/\sqrt{3}m/s$
• D. This is not possible

Answer 1

The correct option is B $\sqrt{3}m/s$

Conserving the momentum in the direction perpendicular to the line of impact i.e. along the inclined plane

$\Rightarrow m{v}_i\cos 60=m{v}_f\cos 30$

$\Rightarrow 3/2=\sqrt{3}{v}_f/2$

$\Rightarrow v_f=\sqrt{3}m/s$

Hence, correct answer is option $B$