Question Number 24178 by NECx last updated on 13/Nov/17
$${A}\:{block}\:{is}\:{released}\:{from}\:{rest}\:{at}\:{the} \\ $$$${top}\:{of}\:{a}\:{frictionless}\:{incline} \\ $$$${plane}\:\mathrm{16}.\mathrm{00}{m}\:{long}.{It}\:{reaches}\:{the} \\ $$$${bottom}\:\mathrm{4}.\mathrm{0}{s}\:{later}.{A}\:{second}\:{block} \\ $$$${is}\:{projected}\:{up}\:{the}\:{plane}\:{from}\:{the} \\ $$$${bottom}\:{at}\:{the}\:{instant}\:{the}\:{first}\:{one} \\ $$$${is}\:{released}\:{in}\:{such}\:{a}\:{way}\:{that}\:{it} \\ $$$${returns}\:{to}\:{the}\:{bottom}\:{simultaneously} \\ $$$${with}\:{the}\:{first}\:{block}.{Find}: \\ $$$$\left.{a}\right){the}\:{acceleration}\:{of}\:{each}\:{block} \\ $$$${on}\:{the}\:{incline}\:{plane} \\ $$$$\left.{b}\right){the}\:{initial}\:{velocity}\:{of}\:{the}\:{first} \\ $$$${block}. \\ $$$$\left.{c}\right){how}\:{far}\:{up}\:{the}\:{incline}\:{plane} \\ $$$${did}\:{the}\:{second}\:{block}\:{travel}. \\ $$$$\left.{d}\right){What}\:{angle}\:{does}\:{the}\:{plane}\:{makes} \\ $$$${with}\:{the}\:{horizontal}. \\ $$$$\left({g}=\mathrm{10}{m}/{s}^{\mathrm{2}} \right) \\ $$
Commented by NECx last updated on 14/Nov/17
$${please}\:{I}\:{ve}\:{issues}\:{with}\:{this}\:{question} \\ $$
Commented by ajfour last updated on 14/Nov/17
Commented by ajfour last updated on 14/Nov/17
$${Let}\:{block}\:{B}\:{was}\:{projected}\:{with} \\ $$$${initial}\:{velocity}\:\boldsymbol{{u}}. \\ $$$$\boldsymbol{{s}}_{\boldsymbol{{A}}} ={l}\:\:{and}\:\boldsymbol{{s}}_{\boldsymbol{{B}}} =\mathrm{0}\:\:,\:{in}\:{a}\:{time}\:{of}\:\mathrm{4}{s}. \\ $$$$\Rightarrow\:\frac{\mathrm{1}}{\mathrm{2}}\left({g}\mathrm{sin}\:\theta\right){t}^{\mathrm{2}} \:=\:{l}\:\:\:{and} \\ $$$$\:−{ut}+\frac{\mathrm{1}}{\mathrm{2}}\left({g}\mathrm{sin}\:\theta\right){t}^{\mathrm{2}} \:=\:\mathrm{0} \\ $$$${or}\:\:\:\:\Rightarrow\:\:\mathrm{8}{g}\mathrm{sin}\:\theta\:=\mathrm{16} \\ $$$$\:\:\:\mathrm{sin}\:\theta\:=\frac{\mathrm{1}}{\mathrm{5}}\:\:{or}\:\:\theta\:=\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{5}}\right) \\ $$$$\:\:\:\:\Rightarrow\:\:\mathrm{4}{u}\:=\mathrm{16} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{u}}\:=\:\mathrm{4}{m}/{s}\:. \\ $$$$\mathrm{0}={u}^{\mathrm{2}} +\mathrm{2}\left({g}\mathrm{sin}\:\theta\right){s}_{{up}\:{the}\:{incline}} \\ $$$${s}_{{up}\:{the}\:{incline}} =\frac{{u}^{\mathrm{2}} }{\mathrm{2}{g}\mathrm{sin}\:\theta}\:=\frac{\mathrm{16}×\mathrm{5}}{\mathrm{20}×\mathrm{1}}\:=\mathrm{4}{m}\:. \\ $$$${Acceleration}\:{of}\:{both}\:{blocks}\:{down} \\ $$$${the}\:{incline}\:{is}\:{mg}\mathrm{sin}\:\theta/{m}\:=\:{g}\mathrm{sin}\:\theta \\ $$$${As}\:{already}\:{found}\:{above}\:\mathrm{sin}\:\theta=\frac{\mathrm{1}}{\mathrm{5}} \\ $$$${so}\:{angle}\:{of}\:{incline}\:{is}\:\theta=\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{5}}\right). \\ $$
Commented by NECx last updated on 14/Nov/17
$${wow}....\:{Thanks} \\ $$$$ \\ $$
Commented by NECx last updated on 14/Nov/17
$${oh}.....\:{i}\:{dont}\:{think}\:{you}'{ve}\:{completed} \\ $$$${it}.\:{It}\:{remains}\:\left({a}\right)\:\left({c}\right)\:{n}\:\left({d}\right) \\ $$
Commented by NECx last updated on 15/Nov/17
$${thanks}\:{boss}. \\ $$$$ \\ $$