Question

A ball of mass $m$ moving with velocity $v_0$ collides a wall as shown in figure. After impact it rebounds with a velocity $\frac{3}{4}{v}_0$. The impulse acting on ball during impact is

• A. $-\frac{m}{2}{v}_0\hat{j}$
• B. $-\frac{3}{4}m{v}_0\hat{i}$
• C. $-\frac{5}{4}m{v}_0\hat{i}$
• D. None of these

Answer 1

The correct option is C $-\frac{5}{4}m{v}_0\hat{i}$

By dividing initial velocity vector into components
$v_i=v_0\cos {37}^{\circ }\hat{i}+v_0\sin {37}^{\circ }\hat{j}=\frac{4}{5}{v}_0\hat{i}+\frac{3}{5}{v}_0\hat{j}$
By dividing final velocity vector into components
$v_f=-\frac{3}{4}{v}_0\cos {53}^{\circ }\hat{i}+\frac{3}{4}{v}_0\sin {53}^{\circ }\hat{j}$
$=-\frac{9}{20}{v}_0\hat{i}+\frac{3}{5}{v}_0\hat{j}$
Impulse due to the wall is
$J=m(v_f-v_i)=-\frac{5}{4}m{v}_0\hat{i}$