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 $6m/s$. 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 $g=10m/s^2$ )

Answer 1

Answer: 1.00

In collision $B/wB$ & $C$
friction $b/wA$ & $B$ non impulsive
$mV=2m{V}_1$

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