Physics

Problem

In a coordinate system where East is

+\hat{i}

and North is

+\hat{j}

, a river flows with velocity

\vec{v}_{r} = 3\hat{i}\,\text{m/s}

. A boat's velocity relative to the water is given by

\vec{v}_{br} = 4\hat{j}\,\text{m/s}

. If the boat starts at the origin

(0,0)

and the river width is

100\,\text{m}

, determine the position vector of the boat when it reaches the other bank.