91Ó°ÊÓ

Velocity is the rate of change in position of an item in motion as seen from a specific frame of reference and measured by a specific time standard.

The velocity of the swimmer relative to the water is V_sw= $0.5$m/s.

He is swimming at a velocity perpendicular to the current. We know the distance covered by him in the positive direction

The time is taken by him to cross the river:

$\begin{array}{rcl}V& =& \frac{d}{t}\\ 0.5& =& \frac{25}{t}\\ t& =& 50s\end{array}$

The total time taken to cross the river is $50$s.

The velocity of the water w.r.t earth:

$\begin{array}{rcl}{V}_{we}& =& \frac{d}{t}\\ & =& \frac{40}{50}\\ & =& 0.8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.\end{array}$

The velocity of the water will be $0.8$m/s

The velocity will be calculated by the following equation:

$\begin{array}{rcl}t& =& 50s\\ D& =& \sqrt{{25}^2+{40}^2}\\ D& =& 47.2m\end{array}$

Using the above equation, we can calculate the speed:

$\begin{array}{rcl}V& =& \frac{d}{t}\\ & =& \frac{47.2}{50}\\ & =& 0.94\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.\end{array}$

The velocity of the swimmer w.r.t his friend at rest on the ground is$0.94$m/s.