91Ó°ÊÓ

The given data can be listed below.

Relative velocity is defined as the velocity of an object relative to another observer. It is the time rate of change of relative position of one object with respect to another object.

Relative speed refers to the speed of one thing in motion or at rest in relation to another object in motion or at rest.

The x-components for canoe velocity relative to earth are given by,

$\begin{array}{rcl}{v}_{ce,x}& =& v_{ce}\cos {45}^o\\ & =& 0.283m/s\end{array}$

The y-component of canoe velocity relative to earth are given by,

$\begin{array}{rcl}{v}_{ce,y}& =& v_{ce}\sin {45}^o\\ & =& 0.283m/s\end{array}$

The canoe velocity relative to the river is given by,

role="math" localid="1659674806621" $v_{cr}=v_{ce}-v_{re}$

Here, v_ce is the velocity of the canoe relative to the earth and v_re is the velocity of the river relative to the earth.

The x-component of canoes velocity relative to the river is given by,

$v_{cr,x}=v_{ce,x}-v_{re,x}$

Here, v_ce,x is the horizontal component of canoe velocity relative to the earth, and v_re,x is the horizontal component of river velocity relative to earth.

Substitute all the values in the above,

$\begin{array}{rcl}{v}_{cr,x}& =& 0.283m/s-0.5m/s\\ & =& 0.217m/s\end{array}$

The y-component of canoes velocity relative to river is given by,

$v_{cr,y}=v_{ce,y}-v_{re,y}$

Here, v_ce,y is the vertical component of canoe velocity relative to earth, and v_re,y is the vertical component of river velocity relative to the earth.

Substitute all the values in the above equation.

$\begin{array}{rcl}{v}_{cr,y}& =& 0.283m/s-0m/s\\ & =& 0.283m/s\end{array}$

The net velocity of the canoe relative to the river is given by,

$v=\sqrt{{\left(v_{cr,x}\right)}^2+{\left(v_{cr,y}\right)}^2}$

Substitute all the values in the above,

$\begin{array}{rcl}v& =& \sqrt{{\left(-0.217m/s\right)}^2+{\left(0.283m/s\right)}^2}\\ & =& \sqrt{0.047089+0.080089}\\ & =& 0.357m/s\end{array}$

The direction of velocity is given by,

$\mathrm{θ}={\tan }^{-1}\left(\frac{v_{cr,y}}{v_{cr,x}}\right)$

Substitute all the values in the above,

$\begin{array}{rcl}\mathrm{θ}& =& {\tan }^{-1}\left(\frac{0.283}{0.217}\right)\\ & =& 52.{52}^o\end{array}$

Hence, the velocity of canoe relative to river is 0.357m/s at 52.52^om/s in southwest direction relative to river.