Question

A particle of mass m has a velocity $-v_0\hat{i}$. while a second particle of same mass has a velocity $v_{0}j$. After the particles collide, first particle is found to have a velocity $\frac{-1}{2}{v}_0\hat{i}$ then the velocity of other particle is

• A. $\frac{-1}{2}{v}_0\hat{i}+v_0\hat{j}$
• B. $\frac{1}{2}{v}_0\hat{i}+v_0\hat{j}$
• C. $v_0\hat{i}+v_0\hat{j}$
• D. $-v_0\hat{i}+v_0\hat{j}$

Answer 1

The correct option is A $\frac{-1}{2}{v}_0\hat{i}+v_0\hat{j}$

Using momentum conservation
Final momentum $=$ Initial momentum

$-\frac{m}{2}{v}_0\hat{i}+m(v_x\hat{i}+v_y\hat{j})=-m{v}_0\hat{i}+m{v}_0\hat{j}$

Comparing

$v_x=-\frac{1}{2}{v}_0\hat{i}$

$v_y=v_0\hat{j}$