Find the resultant (magnitude and directional angle

Question

1. The three displacement vectors in the drawing have magnitudes of A = 5.15 m, B = 5.40 m, and C = 4.20 m. Find the resultant (magnitude and directional angle) of the three vectors by means of the component method. Express the directional angle as an angle above or below the positive or negative x axis. (Assume 𝛼 = 21° and 𝛽 = 54°. Give an answer between 0 and 90°.)

magnitude =	__________ m
direction     +	__________

1. Vector  has a magnitude of 141 units and points 32.0° north of west. Vector  points 69.0° east of north. Vector  points 17.0° west of south. These three vectors add to give a resultant vector that is zero. Using components, find the magnitudes of the following vectors.

(a) vector = ______ units

(b) vector  =______ units

Answer 1

1st, put all your heading into Math angle (0 at x axis and counterclockwise). If you do that then v_x = vcos(θ) and v_y = vsin(θ) and you do not need to worry anymore about trig functions. (v stands for any vector)

2nd, You have 2 equations (x and y displacement component balances) and two unknowns d_c and d_b:

The resultant is 0 which means the x and y resultants are 0

d_ax + d_bx + d_cx = 0 or d_acos(θ_a) + d_bcos(θ_b) + d_ccos(θ_c) = 0

Do the same for y

3rd: solve simultaneous equation in d_b and d_c

I answered the 2nd question.

The first is standard:

1) math angles

2) find x and y resultants

3) combined d - sqrt(d_x² + d_y²) and θ = tan^-1(d_y/d_x) (add 180 if d_x < 0) Redefine angle as a heading.