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Applications based on the Relative Velocity in a Plane #8211; Some applications based on relative velocity are described below: (i) To cross the river of width d along the shortest path Shortest path is PQ , the boat must move along PR making an angle (90° + θ) with the direction of the stream such that the direction of the resultant velocity v is along PQ (see figure). is given by, t = d/v = d/√v<sub>b</sub><sup>2</sup> #8211; v<sub>w</sub><sup>2</sup> where, v<sub>w</sub> = Speed of stream flow and v<sub>b</sub> = Speed of the boat. (ii) To cross the river in the shortest time The shortest time is given by, t = d/v<sub>b</sub>. At this time, boat will reach point S on the opposite bank of the river at a distance x from Q. We can write, x = dtanθ = v<sub>w</sub>/v<sub>b</sub> ⇒ x = d(v<sub>w</sub>/v<sub>b</sub>) x is also called drift.
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