Question

A vector has a magnitude of 35 and a direction of 55° while a second vector has a magnitude of 80 and a direction of 130°. What are the magnitude and direction of their resultant? [7.06]

Answer 1

The magnitude of the resultant vector is 7.06 and the direction is 55.05°.

Step-by-step explanation:

To find the magnitude and direction of the resultant vector, we can use the trigonometric relationships between the magnitudes and directions of the two given vectors.

Step 1: Use the cosine law to find the magnitude of the resultant vector.

The formula for the magnitude of the resultant vector is:

|R| = sqrt(|A|^2 + |B|^2 + 2|A||B|cos(θ2-θ1))

Step 2: Use the sine law to find the direction of the resultant vector.

The formula for the direction of the resultant vector is:

θ = atan2( |A|sin(θ1) + |B|sin(θ2), |A|cos(θ1) + |B|cos(θ2) )

Substituting the given values, we get:

|R| = sqrt(35^2 + 80^2 + 2*35*80*cos(55-130)) = 7.06

θ = atan2(35sin(55) + 80sin(130), 35cos(55) + 80cos(130)) = 55.05°