Answer:
Direction (Standard Position): 306.87° SE
Speed: 5 m/s
Explanation:
Part 1: Direction Angle
The direction angle for a vector
can be found by using the formula
and then accounting the reference angle for the quadrant the vector is located in:
Since
is located in Quadrant IV, then the direction angle must also be located in Quadrant IV. Thus, the true direction angle is
:
This means that the direction the boat is traveling in standard position is 306.87° SE.
Part 2: Speed (Magnitude)
To determine the speed of the vector, we must determine its magnitude, which can be defined as
, thus:
This means that the speed of the boat is 5 m/s