Final answer:
The magnitude and direction of the resultant vector can be found using analytical methods. The magnitude of vector A can be decomposed into its x and y components using trigonometry, and the same can be done for vector B. By adding the corresponding components of A and B, we find the x and y components of the resultant vector R. The magnitude of R can be found using the Pythagorean theorem, and the direction can be calculated using trigonometry.
Step-by-step explanation:
To find the magnitude and direction of the resultant vector, we can use analytical methods. First, we can decompose the given vectors into their x and y components. Vector A has a magnitude of 50 and a direction of 30°, so its x component is 50 * cos(30°) and its y component is 50 * sin(30°). The x component of A is 50 * cos(30°) = 50 * 0.866 = 43.3, and the y component of A is 50 * sin(30°) = 50 * 0.5 = 25.
Similarly, vector B has a magnitude of 60 and a direction of 150°. Its x component is 60 * cos(150°) = 60 * -0.866 = -51.96, and its y component is 60 * sin(150°) = 60 * -0.5 = -30.
To find the x and y components of the resultant vector R, we can add the corresponding components of vectors A and B: Rx = 43.3 - 51.96 = -8.66, and Ry = 25 - 30 = -5.
The magnitude of the resultant vector R can be found using the Pythagorean theorem: |R| = sqrt(Rx^2 + Ry^2) = sqrt((-8.66)^2 + (-5)^2) = sqrt(74.7956 + 25) = sqrt(99.7956) ≈ 9.99.
The direction of the resultant vector R can be found using trigonometry. The direction of R can be found by taking the arctan of Ry/Rx, since R = arctan(Ry/Rx) = arctan(-5/-8.66) = arctan(0.577) ≈ 29.6°.