Question

Final velocities along line of impact.

Answer 1

Let $v_1$ and $v_2$ be the final velocity of A and B respectively then, by conservation of momentum along line of impact
$2\left(4cos{30}^{\circ }\right)-4\left(2cos{30}^{\circ }\right)=2\left(v_1\right)+4\left(v_2\right)$ or $0=v_1+2v_2$ ..... (1)
By coefficient of restitution, $e=\frac{velocityofseparationalongLOI}{velocityofapproachalongLOI}$
or $\frac{1}{3}=\frac{v_2-v_1}{4cos{30}^{\circ }+2cos{30}^{\circ }}$ or $v_2-v_1=\sqrt{3}$ ..... (2)
from the above two equations, $v_1=\frac{-2}{\sqrt{3}}m/s$ and $v_2=\frac{1}{\sqrt{3}}m/s$.