Question

Two masses, $m_1$ and $m_2$ were moving in opposite direction with speeds of $20\text{m/s}$ and $10\text{m/s}$ respectively. They collide and $m_1$ moves with $15\text{m/s}$ after collision in its same direction as of before collision. What is the speed and direction of the second particle after collision, if the coefficient of restitution is $2/3?$

• A. $35\text{m/s}$ in same direction as of first particle
• B. $20\text{m/s}$ in same direction as of first particle
• C. $35\text{m/s}$ in opposite direction as of first particle
• D. $20\text{m/s}$ in opposite direction as of first particle

Answer 1

The correct option is A $35\text{m/s}$ in same direction as of first particle

The coefficient of restitution is given by,

$e=\frac{\text{separation speed}}{\text{approach speed}}=\frac{v_2-v_1}{u_1-u_2}=\frac{2}{3}$

$\Rightarrow \frac{v_2-15}{20-(-10)}=\frac{2}{3}$

$\Rightarrow 3v_2-45=60$

$\therefore v_2=35\text{m/s}$

As $v_2$ comes out to be positive, so both $m_1$ and $m_2$ will travel in the same direction after collision.

Hence, option $\left(A\right)$ is the correct answer.