Notes

To Cross the River of Width d along the Shortest Path in Relative Velocity in a Plane…

To Cross the River of Width d along the Shortest Path in Relative Velocity in a Plane 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).
Given by, t = d/v = d/√v_b² – v_w²
where, v_w = Speed of stream flow and v_b = Speed of the boat.