Add the following vectors using trigonometry (i.e. cosine and sine laws).
9 N on a heading of [S2°W] and 11 N on a heading of [N31°W].
To add the vectors using trigonometry, we need to break down each vector into its horizontal and vertical components. We can then add the horizontal components together and the vertical components together separately to find the resultant vector.
Let's start with the first vector: 9 N on a heading of [S2°W].
Step 1: Finding horizontal and vertical components.
To find the horizontal and vertical components, we need to use the cosine and sine laws.
The horizontal component can be found using the cosine law:
Horizontal component = Magnitude of vector * cos(angle)
Horizontal component = 9 N * cos(2°)
Similarly, the vertical component can be found using the sine law:
Vertical component = Magnitude of vector * sin(angle)
Vertical component = 9 N * sin(2°)
Step 2: Repeat the steps for the second vector: 11 N on a heading of [N31°W].
Horizontal component = 11 N * cos(31°)
Vertical component = 11 N * sin(31°)
Step 3: Add the horizontal and vertical components together:
Horizontal component of the resultant vector = horizontal component of vector 1 + horizontal component of vector 2
Vertical component of the resultant vector = vertical component of vector 1 + vertical component of vector 2
Finally, you can use the Pythagorean theorem to find the magnitude of the resultant vector:
Magnitude of resultant vector = sqrt((Horizontal component of resultant vector)^2 + (Vertical component of resultant vector)^2)
And, to find the angle of the resultant vector, you can use the inverse tangent function:
Angle of resultant vector = tan^(-1)(Vertical component of resultant vector / Horizontal component of resultant vector)
Plug in the values and perform the calculations step by step to find the final answer.