Notes

Applications based on the Relative Velocity in a Plane…

Applications based on the Relative Velocity in a Plane – 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_b² – v_w² where, v_w = Speed of stream flow and v_b = Speed of the boat.
(ii) To cross the river in the shortest time The shortest time is given by, t = d/v_b. 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_w/v_b ⇒ x = d(v_w/v_b) x is also called drift.