Question

A ball of mass $m$ strikes a rigid wall with speed $u$ at an angle of $30^{°}$ and get reflected with the same speed and at the same angle as shown in the figure. If the ball is in contact with the wall for time $t,$ then the force acting on the wall is

• A. $\frac{musin30^{\circ }}{t}$
• B. $\frac{2musin30^{\circ }}{t}$
• C. $\frac{mucos30^{\circ }}{t}$
• D. $\frac{2mucos30^{\circ }}{t}$

Answer 1

Answer: (D)

Initial momentum of the ball is
${\vec{p}}_i$ $=mucos30^{\circ }\hat{i}$ $-musin30^{\circ }\hat{j}$
Final momentum of the ball is
${\vec{p}}_f$ $=-mucos30^{\circ }\hat{i}$ $-musin30\hat{j}$
$\therefore$ Change in momentum,
$\Delta \vec{p}$ $={\vec{p}}_f$ $-{\vec{p}}_i$ $=-2mucos30^{\circ }\hat{i}$
Impulse = Change in momentum $=-2mucos30^{\circ }\hat{i}$
As impulse and force are in the same direction, therefore, force on the ball due to the wall is normal to the wall along the negative $x$-axis. Using Newton’s $3^{rd}$ law of motion the force on the wall due to the ball is normal to the wall along the positive $x-$ direction.
$\therefore$ $F=\frac{2mucos30^{\circ }}{t}$