JEE Main 2025 Apr 2 Shift 1, Physics Q6: Motion In Two And Three Dimension

The boat's velocity makes $150°$ with the river-flow direction (east). The component of the boat's velocity across the river is the projection perpendicular to the flow.

If the flow direction is along the +x axis, the boat's velocity vector at $150°$ has y-component:

$$v_{\perp }=27\sin (150°)=27\times \frac{1}{2}=\frac{27}{2}\text{km/h}$$

Time of crossing $=30\text{s}=\frac{1}{120}\text{h}$.

Width of the river:

$$W=v_{\perp }\times t=\frac{27}{2}\times \frac{1}{120}\text{km}=\frac{27}{240}\text{km}=0.1125\text{km}=112.5\text{m}$$

$\therefore$ Option (2) is correct.