9514 1404 393
Answer:
16.9 m/s N 32.9° W
Explanation:
The resultant magnitude can be found from the law of cosines. The internal angle between the boat's heading and the river flow is 135°, so the magnitude of the boat's net speed is ...
v² = 5² +13² -2·5·13·cos(135°) ≈ 285.924
v = 16.9093 . . . . m/s
The angle (α) between the boat's heading and the resultant velocity can be found from the law of sines.
sin(α)/5 = sin(135°)/16.9093
α = arcsin(5/16.9093×sin(135°)) ≈ 12.07°
The boat's actual heading will be this angle less than the 45° angle the heading makes with due North.
45° -12.07° = 32.93°
The boat's velocity with respect to shore is about ...
16.9 m/s N 32.9° W