Theory question 105
Vectors(a) Write the following as column vectors:
r = (10 N, 090°)
q = (8 N, 135°)
(b) use your answer in 5(a) to find (r + q)
Show the model answer
Model answer
Using bearings, a force (F, θ) = (F sin θ / F cos θ) (east component / north component)
(a) r = (10 sin 90° / 10 cos 90°) = (10 / 0)
q = (8 sin 135° / 8 cos 135°) = (4√2 / −4√2) ≈ (5.66 / −5.66)
(b) r + q = (10 + 4√2 / −4√2) ≈ (15.66 / −5.66)
Explanation
Resolve each force into east and north components using its bearing; then add component by component.