Q 11-03-173JEE MainJEE Main 2025 (2 Apr, Shift 1)Easy
A river is flowing from west to east direction with a speed of $9\ \text{km h}^{-1}$. A boat capable of moving at a maximum speed of $27\ \text{km h}^{-1}$ in still water crosses the river in half a minute, while moving with maximum speed at an angle of $150^\circ$ to the direction of river flow. The width of the river is:
Answer: (B) $112.5\ \text{m}$
Only the component of the boat's velocity (relative to water) perpendicular to the flow carries it across; the river's velocity is along the bank and does not help.
$$v_\perp = 27\sin150^\circ = 13.5\ \text{km/h} = 13.5\times\frac{5}{18} = 3.75\ \text{m/s}$$
$$\text{width} = v_\perp t = 3.75 \times 30 = 112.5\ \text{m}$$
Solution by Sreeraj P, M.Sc Physics