Question Number 131012 by mohammad17 last updated on 31/Jan/21
Commented by mohammad17 last updated on 31/Jan/21
$${help}\:{me}\:{sir} \\ $$
Answered by mr W last updated on 31/Jan/21
Commented by mohammad17 last updated on 31/Jan/21
$${can}\:{you}\:{complete}\:{the}\:{solution}\:{sir} \\ $$
Commented by mr W last updated on 31/Jan/21
$${b}={width}\:{of}\:{gate}=\mathrm{1}.\mathrm{5}{m} \\ $$$${F}_{\mathrm{1}} =\frac{\rho{gbH}^{\mathrm{2}} }{\mathrm{2}} \\ $$$${F}_{\mathrm{2}} =\rho{gbHL} \\ $$$${the}\:{gate}\:{begins}\:{to}\:{open}\:{when} \\ $$$${F}_{\mathrm{1}} ×\frac{{H}}{\mathrm{3}}\geqslant{F}_{\mathrm{2}} ×\frac{{L}}{\mathrm{2}} \\ $$$$\frac{\rho{gbH}^{\mathrm{2}} }{\mathrm{2}}×\frac{{H}}{\mathrm{3}}\geqslant\rho{gbHL}×\frac{{L}}{\mathrm{2}} \\ $$$$\Rightarrow{H}\geqslant\sqrt{\mathrm{3}}{L}=\mathrm{20}\sqrt{\mathrm{3}}\approx\mathrm{34}.\mathrm{6}\:{cm} \\ $$$$\Rightarrow{h}\geqslant\mathrm{100}+\mathrm{34}.\mathrm{6}=\mathrm{134}.\mathrm{6}\:{cm} \\ $$
Commented by mohammad17 last updated on 31/Jan/21
$${thank}\:{you}\:{sir} \\ $$