Question

50 Two boats A, B are rowed perpendicular to each other with identical speeds of 8 km/h (with respect to water). The relative velocity of A with respect to B $\vec{v}_{A/B}$ makes an angle of $\theta$ with the flow direction. $\theta$ =

• A. 15°
• B. 30°
• C. 45°
• D. 75°

Answer 1

Answer: (C)

45°

Answer 2

When computing the relative velocity of boat A with respect to boat B, note that both boats are rowed with the same speed (8 km/h relative to water) in directions that are perpendicular. Their actual (ground) velocities are the sums of their respective rowing (water‐frame) velocities and the common water flow (6 km/h eastward). In taking the difference (v_A – v_B), the water flow cancels out. Thus, the relative velocity equals the difference of two perpendicular vectors of equal magnitude. The difference of such vectors bisects the 90° angle between them, giving an angle of 45° relative to the flow.