Boatman Crossing a River – Rankers Physics

Relative Motion in Two Dimension: Practice Problem & Solution

A river \(2\text{ km}\) wide flows at the rate of \(2\text{km/h}\). A boatman who can row a boat at a speed of \(6\text{ km/h}\ in still water, goes a distance of \(2\text{ km}\ upstream and then comes back. The time taken by him to complete his journey is
60 min
45 min
80 min
90 min

Solution Explained:

To solve this problem, we apply the core principles of Relative Motion in Two Dimension. Understanding the underlying formula is key to arriving at the correct answer below:

Boat speed in still water \(v_b = 6\text{ km/h}\), river speed \(v_r = 2\text{ km/h}\). Upstream speed \(v_u = v_b - v_r = 4\text{ km/h}\). Downstream speed \(v_d = v_b + v_r = 8\text{ km/h}\). Time upstream \(t_u = 2\text{ km} / 4\text{ km/h} = 0.5\) hours. Time downstream \(t_d = 2\text{ km} / 8\text{ km/h} = 0.25\) hours. Total time = \(0.5 + 0.25 = 0.75\) hours = \(45\) minutes.

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