A powerboat heads due northwest at 13 m/s with respect to the water across a river that flows due north at 5.0 m/s.

What is the velocity (both magnitude and direction) of the motorboat with

respect to the shore?

9514 1404 393

  16.9 m/s N 32.9° W

Step-by-step 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

shift 4 units up, and 1 unit left.

it will translate f(x) = 3^x to g(x) = 3^(x+1) + 4