Question

The diagram shows vectors that are not perpendicular to one another.

Three vectors are drawn tail to tip method in the x y plane. Vector labeled E starts at the origin and is drawn in the northeast direction. The second vector is labeled F and drawn in the south southeast direction. The third is labeled G and drawn in the north northeast direction. X and Y components are drawn for each vector along the x and y axis.

The data table shows the magnitudes of the components of each displacement vector.

A 2 column table with 5 rows. The first column is labeled Component with entries E Subscript x Baseline, F Subscript x Baseline, G Subscript x Baseline, E Subscript y Baseline, F Subscript y Baseline, G Subscript y Baseline. The second column is labeled Magnitude in centimeters with entries 2, 4, 2, 2, 1, 3.

What is the angle of the resultant vector, rounded to the nearest tenth?

0.1°
10.0°
36.9°
41.1°

Answer 1

36.9°

Reason: Rx = 2 + 4 + 2 = 8 cm, Ry = 2 + 1 + 3 = 6 cm, so θ = arctan(Ry/Rx) = arctan(6/8) ≈ 36.9°.