Motion in a Plane

Concept:For minimum crossing time, the boat must head perpendicular to the river flow, maximizing the velocity component across the river.Explanation:Convert speeds to m/s: $v_r = 18\text{ km/h} = 5\text{ m/s}$, $v_b = 36\text{ km/h} = 10\text{ m/s}$. River width $d = 200\text{ m}$.Time for one crossing: $t_1 = \frac{d}{v_b} = \frac{200}{10} = 20\text{ s}$. Round trip time: $T = 2 \times 20 = 40\text{ s}$.Drift per crossing: $x_1 = v_r \times t_1 = 5 \times 20 = 100\text{ m}$. Total drift after round trip: $x = 2 \times 100 = 200\text{ m}$.Thus minimum time is $40\text{ s}$ and displacement along river bank is $200\text{ m}$.Answer:$40\text{ s}$ and $200\text{ m}$ (Option C).