A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches $30^o$, the box starts to slip and slides $4.0\, m$ down the plank in $4.0\,s$. The coefficients of static and kinetic friction between the box and the plank will be, respectively
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Coefficient of static friction.
$\mu_{s}=\tan 30^{\circ}=\frac{1}{\sqrt{3}}=0.6$
$a=g \sin 30^{\circ}-\mu_{k} g \cos 30^{\circ}$
$S=u t+\frac{1}{2} a t^{2}$
$\Rightarrow 4=\frac{1}{2}\left[\frac{\mathrm{g}}{2}-\frac{\mu_{\mathrm{k}} \mathrm{g} \sqrt{3}}{2}\right] \times 16 \Rightarrow \mu_{\mathrm{k}}=0.5$
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