Question

A particle of mass $m$ moving with a velocity of $(4\hat{i}-\hat{j})m/s$ strikes a fixed wall and finally moves with a velocity of $(3\hat{i}+2\hat{j})m/s$. Find
(a) the impulse received by the particle
(b) the coefficient of restitution between them in the collision

Answer 1

Impulse $=m({\overrightarrow{v}}_f-{\overrightarrow{v}}_i)=m(3\hat{i}+2\hat{j}-4\hat{i}-\hat{j})=m(-\hat{i}+3\hat{j})N-s$
(b) Since coefficient of restitution is considered along common normal thus calculating the component of velocities along common normal $e=v_2/v_1$
Now $-e=\frac{(3\hat{i}+2\hat{j})(-\hat{i}+3\hat{j})}{(4\hat{i}-\hat{j})(-\hat{i}+3\hat{j})}\Rightarrow -e=\frac{-3+6}{-4-3}\Rightarrow e=\frac{3}{7}$