Relative Velocity In River Crossing

As described in NCERT Class 11, Chapter 4 (Motion in a Plane), when a swimmer heads directly across a river, the swimming velocity is perpendicular to the river current, so the two velocities combine as perpendicular vectors. The resultant speed relative to the bank is the vector sum: √(4² + 3²) = √(16 + 9) = √25 = 5 m/s. The option 7 m/s wrongly adds the speeds arithmetically as if they were along the same line. The option 1 m/s subtracts them, which would apply only to anti-parallel velocities. The option 3.5 m/s incorrectly averages the two speeds. Plausibility check: the resultant of two perpendicular vectors must be larger than either component but smaller than their direct sum, so it must lie between 4 and 7 m/s; the value 5 m/s correctly falls in this range and forms a classic 3-4-5 right triangle, confirming the vector addition.