A swimmer wants to cross 500 m wide river flowing at 5km/h. his speed with respect to water is 3km/h. the man has to reach the point directly opposite to his starting point. If he reaches the other shore somewhere else, he has to walk to the point . Find the minimum distance that he has to walk. (swimmer makes an angle thita)

Question

anonymous · Answer

The swimmer makes angle thita with the river flow .Therefore 

component of  velocity in horizontal dir.=5+3cos thita

component of  velocity in vertical dir.=3sin thita

Therefore,time to cross river =0.5/3sin thita=1/6sin thita

min. distance swimmer has to walk =(5+3cos thita)(1/6sin thita)=H..............(1)

for min. distance dH/d thita =0
why?? ------------- dH/d thita =0 ??

anonymous · Answer

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