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Question

Find the magnitude and the direction of vector G as a sum of two vectors D and E by

going through the following steps.

a. D = 10 m at 37 ̊. Find Dx and Dy.

b. E = 20 m at 25 ̊. Find Ex and Ey.

c. Find Gx = Dx + Ex

d. Find Gy = Dy + Ey

e. Find the magnitude of G from its components

f. Find the direction of G.

Answer 1

Using trig ratios on the first figure, cos(θ) = adj/hyp so:

cos(37°) = D_x/D

cos(37°) = Dx/10

Dx = 10cos(37°) = 7.986

and sin(θ) = opp/hyp so:

sin(37°) = Dy/D

sin(37°) = Dy/10

Dy = 10sin(37°) = 6.018

In the same way, using the same trig ratios on the second figure:

Ex = 20cos(25°) = 18.126

Ey = 20sin(25°) = 8.452

Therefore Gx = 7.986 + 18.126 = 26.113 and Gy = 6.018 + 8.452 = 14.471

G = √(26.113² + 14.471²) = √891.259 = 29.854 or, rounded off, G = 30

The direction of G is found by again using trig ratios. The opposite side (Gy) = 14.471 and the adjacent side (Gx) = 26.113 and since tan(θ) = opp/adj then tan(θ) = 14.471/26.113 or θ = tan^-1(14.471/26.113) = 29°