Question

A man rows across a river with velocity 8 km h-1. if his resultant velocity is 10 km h-1 then what is the speed of river water?

Answer 1

Resultant velocity = √(velocity of man)²+(velocity of river)²
10 = √8² + (velocity of river)²
=> velocity of river = √10²-8² = 6m/s

Answer 2

The boat velocity combined with the river velocity gives the resultant velocity.  

Since, the man rows the boat across the river which is perpendicular to the flow of river.  

If $v_1$ is the velocity of the boat and $v_2$ is the velocity of the river, then we can apply Pythagoras theorem to find the resultant velocity.  

                           $v_{ 3 }^{ 2 }\quad =\quad v_{ 1 }^{ 2 }\quad +\quad v_{ 2 }^{ 2 }\\10^{ 2 }\quad =\quad { 8 }^{ 2 }\quad +\quad v_{ 2 }^{ 2 }\\100\quad -\quad 64\quad =\quad v_{ 2 }^{ 2 }\\v_{ 2 }\quad =\quad \sqrt { 36 }\\v_{ 2 }\quad =\quad 6\quad Km/hr$