Question

Two balls are rolling on a flat smooth table. The velocity components of one are $\hat{i}$ and $\sqrt{3}\hat{j}$ and that of the other are $2\hat{i}$ and $2\hat{j}$. If both start moving simultaneously from the same point. What is the angle between their paths-

• A. $15$
• B. $300$
• C. $45$
• D. $600$

Answer 1

The correct option is A $15$

angle of $1^{st}$ ball with horizontal $\theta =ta{n}^{-1}\frac{u_y}{u_x}=ta{n}^{-1}\sqrt{3}={60}^o$

angle of $2^{nd}$ ball $\varphi =ta{n}^{-1}\frac{v_y}{v_x}=ta{n}^{-1}1={45}^o$

angle between their paths is $\theta -\varphi =60-45={15}^o$