Question

Two balls with masses $m_1$ = 3 kg and $m_2$ = 5 kg have initial velocities $v_1$ = 5 m/s = $v_2$ in the directions as shown in figure. They collide at the origin. Find the velocity of the COM 3 seconds before collision?

• A. -(12$\hat{i}-15\hat{j}$) m/s
• B. (-12 $\hat{i}+15\hat{j}$) m/s
• C. (-12 $\hat{i}+15\hat{j}$) m/s
• D. (-15 $\hat{i}-12\hat{j}$) m/s

Answer 1

The correct option is B

(-12 $\hat{i}+15\hat{j}$) m/s

The given time is of no consequence since $V_{COM}$ is fixed for all times as there is no external force acting on the system of 2 particles.
$V_{com}{)}_x=\frac{m_1(v_1{)}_x+m_2(v_2{)}_x}{m_1+m_2}=\frac{\left(3\right)(-5cos{37}^{\circ })+5\left(0\right)}{8}=15m/s(V_{com}{)}_x=\frac{m_1(V_1{)}_y+m_2(V_2{)}_y}{m_1+m_2}=\frac{3(-5sin{37}^{\circ })+5\left(5\right)}{8}=+2m/s{\overrightarrow{v}}_{com}=(-15\hat{i}+2\hat{J})m/s$