Question

Board $A$ is placed on board $B$ as shown. Both boards slide, without moving with respect to each other, along a frictionless horizontal surface at a speed $6 \,m / s$. Board $B$ hits a resulting board $C$ "head-on". After the collision, boards $B$ and $C$ stick together and board $A$ slides on top of board $C$ and stops its motion relative to $C$ in the position shown on the diagram. What is the length (in $m$) of each board? All three boards have the same mass, size and shape. The coefficient of kinetic friction between boards $A$ and $C$ and between boards $A\, \&\, B$ is $0.3$. (here $g=10\, m / s ^{2}$ )

Answer 1

In collision $B / w B$ & $C$
friction $b / w A$ & $B$ non impulsive
$mV =2 mV _{1}$

$\operatorname{wrt}(B+C) V^{2}=u^{2}+2\, a s$
$0=(3)^{2}+2\left(-\frac{3 \mu g}{2}\right) \Delta x$
$\Delta x=L=\frac{9}{3 \mu g}$
$L=\frac{3}{0.3 \times 10} $
$\Rightarrow L=1 \,m$