Question

A boat sails 285 miles south and

then 132 miles west.
What is the direction of the
boat's resultant vector?
Hint: Draw a vector diagram.
Ө 0 = [ ? ]°
Round your answer to the nearest hundredth.
65.15 is the wrong answer so don't put it

Answer 1

65.1 degrees north of east

Explanation:

The boat sails 285 miles south, which means it moves in the direction of south (S) on the diagram. Then it sails 132 miles west, which means it moves in the direction of west (W) on the diagram. We draw a vector diagram to represent the boat's motion (I attached a picture of the diagram)

The boat's motion can be represented by a resultant vector R, which is the vector that connects the starting point to the ending point of the boat's motion. We want to find the direction of this vector.

R^2 = (285 miles)^2 + (132 miles)^2

R = √((285 miles)^2 + (132 miles)^2)

R ≈ 316.2 miles

Now we can use trigonometry to find the angle θ between the resultant vector and the east direction.

tan θ = opposite/adjacent

tan θ = 285 miles / 132 miles

θ = atan(285 miles / 132 miles)

θ ≈ 65.1 degrees

So, the direction of the boat's resultant vector is 65.1 degrees north of east (NE).