a swimmer wishes to cross a 500 m wide river flowing at 5km/hr his speed with respect to water is  3 km/hr .

cthe man has to reach the other shore at da point directly opp to his starting point .if he reaches the other shore sumwere else hw has to walk down to this point find the minimum distance he has to walk ?//

x=distance the swimmer has to walk=(5+3cos@)*0.5/3sin@   (@ is with the horizontal

find dx/d@ =0put value of @to get the ans

the orange colour line represents dirn of head whereas the black line represens dirn of boat

detailed soln:

V_b/g=5+3cos  i+3sin  km/hr

time taken t =0.5km/3sinkm/hr

horizontal distance x=(V_x)*t=(5+3cos)*0.5km/3sinkm/hr

for max/min

dx/d=0

which gives cos=-4/5 sin=3/5

putting the values  x(min)=2/3 km