Velocity of river,
Vr=5 m/min
Velocity of man w.r.t river,
Vm=10 m/min
Let the width of the river be
d and assume the man heads in a direction making angle
θ with the bank of the river.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/932926/original_1.png)
On breaking component of
Vm along and perpendicular to river flow
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/930547/original_5_S.png)
We can see that component
Vmsinθ will be responsible for crossing the river.
Time taken to cross river,
t=width of riverperpendicular component of velocity
∴t=dVmsinθ
For
t to be minimum,
sinθ should be maximum, and maximum value of
sinθ is
1 at
θ=π2=90∘.
∴ Man should head at angle of
90∘ with the bank of river i.e. in North direction.