Question

Homework - Pure Year 1 - Chapter 11B

Vectors
3
force.
Work out the magnitude of the resultant force and the angle this makes with the smaller
8N
60.00
1SN

Answer 1

|F net| = 20.22 N

θ ≈ 19.8°

Explanation:

F net = 15N i + 8cos(60°)N i + 8sin(60°)N j

= 15N i + 8×½N i + 8×√3/2N j

= 15N i + 4N i + 4√3N j

= 19N i + 4√3N j

|F net| = √(19²+(4√3)²) = √(361+48) = √409 ≈ 20.22N

tan(θ) = 4√3 ÷ 19 ≈ 0.36 → θ ≈ arctan(0.36) = 19.8°