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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  0.5 seconds for 1 meter in water and  0.4 seconds for 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.  (a) (i)  with x=20, T=5(√(36+400))=104=10.4 sec  (a)(ii)  with x=0, T=5(√(36))+4×20=110=11 sec  (b)  (dT/dx)=((5x)/(√(36+x^2 )))−4=0  25x^2 =16(36+x^2 )  x^2 =64  ⇒x=8  T_(min) =5(√(36+64))+4×12=98=9.8 sec

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

Commented by TawaTawa last updated on 08/Sep/19

God bless you sir

$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$

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