Question Number 224406 by Tawa11 last updated on 08/Sep/25
Answered by mr W last updated on 09/Sep/25
$${mur}\:\mathrm{sin}\:\theta_{\mathrm{0}} ={mUr} \\ $$$$\Rightarrow{u}\:\mathrm{sin}\:\theta_{\mathrm{0}} ={U} \\ $$$$\frac{{mu}^{\mathrm{2}} }{\mathrm{2}}=\frac{{mU}^{\mathrm{2}} }{\mathrm{2}}+{mgr}\:\mathrm{cos}\:\theta_{\mathrm{0}} \\ $$$$\frac{{u}^{\mathrm{2}} }{\mathrm{2}}=\frac{{u}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}} \:\theta_{\mathrm{0}} }{\mathrm{2}}+{gr}\:\mathrm{cos}\:\theta_{\mathrm{0}} \\ $$$${u}^{\mathrm{2}} \:\mathrm{cos}\:\theta_{\mathrm{0}} =\mathrm{2}{gr} \\ $$$$\Rightarrow{u}=\sqrt{\frac{\mathrm{2}{gr}}{\mathrm{cos}\:\theta_{\mathrm{0}} }}\:\checkmark \\ $$
Commented by mr W last updated on 10/Sep/25
Commented by fantastic last updated on 09/Sep/25
$${why}\:{were}\:{you}\:{inactive}\:{for} \\ $$$${some}\:{days}?? \\ $$
Commented by Tawa11 last updated on 13/Sep/25
$$\mathrm{Thanks}\:\mathrm{sir},\:\mathrm{I}\:\mathrm{appreciate}. \\ $$
Commented by mr W last updated on 13/Sep/25
$${did}\:{you}\:{comfirm}\:{that}\:{the}\:{answer}\:{is} \\ $$$${correct}? \\ $$
Commented by Tawa11 last updated on 14/Sep/25
$$\mathrm{Yes}\:\mathrm{sir}. \\ $$$$\mathrm{they}\:\mathrm{wrote}\:\:\:\:\:\sqrt{\mathrm{2gr}\:\mathrm{cos}\theta_{\mathrm{0}} } \\ $$
Commented by mr W last updated on 14/Sep/25
$${what}\:{do}\:{you}\:{think}\:{is}\:{right}, \\ $$$$\sqrt{\frac{\mathrm{2}{gr}}{\mathrm{cos}\:\theta_{\mathrm{0}} }}\:{or}\:\sqrt{\mathrm{2}{gr}\:\mathrm{cos}\:\theta_{\mathrm{0}} }\:? \\ $$
Commented by fantastic last updated on 07/Oct/25
$${I}\:{also}\:{got} \\ $$$${u}=\sqrt{\frac{\mathrm{2}{gr}}{\mathrm{cos}\:\theta_{\mathrm{0}} }} \\ $$