Question Number 68278 by TawaTawa last updated on 08/Sep/19
Commented by mr W last updated on 08/Sep/19
$${it}\:{is}\:{to}\:{see}\:{that}\:{the}\:{crocodile}\:{takes} \\ $$$$\mathrm{0}.\mathrm{5}\:{seconds}\:{for}\:\mathrm{1}\:{meter}\:{in}\:{water}\:{and} \\ $$$$\mathrm{0}.\mathrm{4}\:{seconds}\:{for}\:\mathrm{1}\:{meter}\:{on}\:{land}.\:{is} \\ $$$${this}\:{true}?\:{because}\:{i}\:{thought}\:{a}\:{crocodile} \\ $$$${is}\:{faster}\:{in}\:{water}\:{than}\:{on}\:{land}.... \\ $$$${let}'{s}\:{assume}\:{the}\:{book}\:{is}\:{right}. \\ $$$$\left({a}\right)\:\left({i}\right) \\ $$$${with}\:{x}=\mathrm{20},\:{T}=\mathrm{5}\sqrt{\mathrm{36}+\mathrm{400}}=\mathrm{104}=\mathrm{10}.\mathrm{4}\:{sec} \\ $$$$\left({a}\right)\left({ii}\right) \\ $$$${with}\:{x}=\mathrm{0},\:{T}=\mathrm{5}\sqrt{\mathrm{36}}+\mathrm{4}×\mathrm{20}=\mathrm{110}=\mathrm{11}\:{sec} \\ $$$$\left({b}\right) \\ $$$$\frac{{dT}}{{dx}}=\frac{\mathrm{5}{x}}{\sqrt{\mathrm{36}+{x}^{\mathrm{2}} }}−\mathrm{4}=\mathrm{0} \\ $$$$\mathrm{25}{x}^{\mathrm{2}} =\mathrm{16}\left(\mathrm{36}+{x}^{\mathrm{2}} \right) \\ $$$${x}^{\mathrm{2}} =\mathrm{64} \\ $$$$\Rightarrow{x}=\mathrm{8} \\ $$$${T}_{{min}} =\mathrm{5}\sqrt{\mathrm{36}+\mathrm{64}}+\mathrm{4}×\mathrm{12}=\mathrm{98}=\mathrm{9}.\mathrm{8}\:{sec} \\ $$
Commented by TawaTawa last updated on 08/Sep/19
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$