River-boat Relative Motion

When a swimmer aims directly across a flowing river, the swimming velocity (perpendicular to the bank) and the river current velocity (parallel to the bank) are mutually perpendicular vectors. The resultant velocity relative to the ground is their vector sum, whose magnitude follows from the Pythagorean theorem because the components are orthogonal. The swimmer contributes $4\text{ m/s}$ across the stream and the current contributes $3\text{ m/s}$ downstream. The resultant ground speed is $\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25}=5\text{ m/s}$. The option 7 m/s is wrong because it adds the speeds as if they were along the same line. The option 1 m/s is wrong because it subtracts them, which would apply only to anti-parallel vectors. The option 3.5 m/s is an unsupported average. This applies the NCERT vector-addition treatment of independent perpendicular velocities in river-crossing problems. The crossing time itself depends only on the across-stream component and the river width, while the current solely determines how far downstream the swimmer drifts, illustrating the independence of perpendicular motions. As a check, the resultant exceeds each individual component, which must hold for the sum of two perpendicular vectors, and the swimmer is carried diagonally downstream rather than straight across.