Coplanar forces of magnitudes 60N, 20N, 16N and 14N act at a point in the directions shown in the diagram. [Figure 2.1]

Mark scheme

Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.

1. [M1] Resolving either direction; 3 terms; allow sign errors and allow sin/cos mix
2. [A1] (X =)±(20cos 60-14-16cos50) [=+14.2846.........]
3. [A1] (Y=)±(60-20 sin 60-16sin 50) [= ±30.42278.........]
4. [M1] Attempt to solve for R; one missing term in total; R = √(14.2846...)² + (30.42278...)²
5. [M1] Attempt to solve for θ or a; one missing term in total; θ = tan⁻¹(30.42278.../14.2846...) [= tan⁻¹(2.1297......)] OR a = tan⁻¹(14.2846.../30.42278...) [= tan⁻¹(0.4596......)]
6. [A1] R = 33.6 N; Direction is 64.8° above the 14 N force or 25.2° above the negative x-axis or 25.2° left of the 60 N force or bearing 335° or 115° anticlockwise from the positive x -axis; Both correct. OE; allow 64.9, 25.1; Giving an angle only is insufficient. Direction may be seen on a diagram, with minimum of arrow on resultant. Arrows on both components only is A0 as it doesn't show the direction of the resultant. However the direction is stated, it must be able to be drawn uniquely.