Question

A ball of mass m moving with velocity $v_0$ collides a wall as shown in the 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. $-\frac{3}{7}m{v}_0\hat{i}$

Answer 1

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

$v_i=v_{0}cos{37}^{\circ }\hat{j}+v_{0}sin{37}^{\circ }\hat{j}=\frac{4}{5}{v}_0\hat{i}+\frac{3}{5}{v}_0\hat{j}$
$v_f=-\frac{3}{4}{v}_{0}cos{53}^{\circ }\hat{i}+\frac{3}{4}{v}_{0}sin{53}^{\circ }\hat{j}$
$=-\frac{9}{20}{v}_0\hat{i}+\frac{3}{5}{v}_0\hat{j}$
$J=m(v_f-v_i)=-\frac{5}{4}m{v}_0\hat{i}$