A motorboat is racing towards the north at 25 $kmh^{-1}$ and the water current in that region is 10 $kmh^{-1}$ in the direction of 60$^{\circ}$ east of south. The resultant velocity of the boat is:
-
11 $kmh^{-1}$
-
22 $kmh^{-1}$
-
33 $kmh^{-1}$
-
44 $kmh^{-1}$
B
Correct answer
Explanation
Boat velocity vB = 25 (North). Current vC = 10 (60 deg east of south). East of south is 120 deg from North. Use vector addition: Resultant^2 = 25^2 + 10^2 + 2 * 25 * 10 * cos(120). Resultant^2 = 625 + 100 + 500 * (-0.5) = 725 - 250 = 475. Resultant = sqrt(475) approx 21.8, which is 22.