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 $\angle$ of inclined 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 C $1/\sqrt{3}m/s$

Conserving the momentum, as there are no external forces.
The total Y-momentum of the body gets transferred to inclined plane (as final momentum of ball is only in X)
Inclined plane moves normal to hitting surface.
Thus,
$v_x^{inclined}=v_y^{inclined}\tan \left(\theta \right)$

So, $v_x^{inclined}=3\tan \left(30\right)=\frac{1}{\sqrt{3}}$

and conservation of X-momentum

$v_x^{body}+v_x^{inclined}=0$

So, $v_x^{body}=-\frac{1}{\sqrt{3}}m/s$