Question Number 114223 by mathdave last updated on 17/Sep/20
Answered by mr W last updated on 18/Sep/20
$${a}={g}\left(\mathrm{sin}\:\theta−\mu\:\mathrm{cos}\:\theta\right) \\ $$$${v}_{\mathrm{2}} ^{\mathrm{2}} −{v}_{\mathrm{1}} ^{\mathrm{2}} =\mathrm{2}{as} \\ $$$${v}_{\mathrm{2}} ^{\mathrm{2}} −{v}_{\mathrm{1}} ^{\mathrm{2}} =\mathrm{2}{g}\left(\mathrm{sin}\:\theta−\mu\:\mathrm{cos}\:\theta\right){s} \\ $$$$\Rightarrow\mu=\mathrm{tan}\:\theta−\frac{{v}_{\mathrm{2}} ^{\mathrm{2}} −{v}_{\mathrm{1}} ^{\mathrm{2}} }{\mathrm{2}{gs}\:\mathrm{cos}\:\theta} \\ $$$$\Rightarrow\mu=\mathrm{tan}\:\mathrm{30}°−\frac{\mathrm{30}^{\mathrm{2}} −\mathrm{10}^{\mathrm{2}} }{\mathrm{2}×\mathrm{10}×\mathrm{100}×\mathrm{cos}\:\mathrm{30}°}=\mathrm{0}.\mathrm{115} \\ $$
Commented by mathdave last updated on 18/Sep/20
$${thank}\:,{great}\:{work} \\ $$
Commented by Tawa11 last updated on 06/Sep/21
$$\mathrm{great}\:\mathrm{sir} \\ $$