Question

Vector A⃗ has magnitude 5.00 and is at an angle of 36.9∘ south of east. Vector B⃗ has magnitude 6.40 and is at an angle of 20.0∘ west of north. Choose the positive x-direction to the east and the positive y-direction to the north. Find the components of A⃗ .

Answer 1

Answer:

3.9984i-3.0021j

Step-by-step explanation:

Due to the fact that we are only asked for the components on A, we will focus on that information.

The first thing we need to do is to dimension the magnitud of A as a hypotenuse of a right triangle. As the vector is ponting in south-east direction, we can asume that it´s (i) component will be positive and it´s (j) component will be negative.

Now, using trigonometric functions we can find the components of the vector A by multiplying the magnitude by -sin(x) for (j) and cos(x) for (i).

-5sin(36.9)=-3.0021

(this component is negative due to the fact that the vector is pointing down)

5cos(36.9)= 3.9984

Now we write in the correct notation x(i) + y(j)

3.9984i-3.0021j