Physics - Kinematics Question with Solution | TestHub

To cross the river in the shortest possible time, the boat must head perpendicular to the river flow. Let the river flow along the x-axis (east) and the boat aim along the y-axis (north). The velocity of the river relative to the ground is ${\vec{v}}_{wg}=3\hat{i}\text{m/s}$. The velocity of the boat relative to the water is ${\vec{v}}_{bw}=4\hat{j}\text{m/s}$. The velocity of the boat relative to the ground is given by the vector sum ${\vec{v}}_{bg}={\vec{v}}_{bw}+{\vec{v}}_{wg}=4\hat{j}+3\hat{i}$. The magnitude of this velocity is $|{\vec{v}}_{bg}|=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5\text{m/s}$.