Coplanar forces of magnitudes 45N, 28N, 72N and 35N act at a point in the directions shown in the diagram. [Figure 3.1] Find, in either order, the magnitude and direction of the resultant force.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

1. [*M1] For attempt to resolve in any direction to form an equation or expression Correct number of terms; allow sign errors and sin/cos mix ONLY.
2. [A1] Vertically: (Y=) ±(45+28sin35-72sin50-35sin60) +24.405948 ...
3. [A1] Horizontally: (X =) ±(28cos35+72cos 50-35 cos 60) ±51.716965 ...
4. [DM1] Attempt to solve for R from equations with the correct number of relevant terms (only sign errors and sin/cos mix allowed).
5. [DM1] Attempt to solve for θ or α from equations with the correct number of relevant terms (only sign errors and sin/cos mix allowed).
6. [A1] R = 57.2 N Both correct. Direction is 25.3° below the positive x-direction or bearing 115° Giving an angle only is insufficient. Direction may be seen on a diagram, with minimum of arrow on resultant OE. May give direction relative to one of the given forces e.g. 24.7° anticlockwise from the 72 N force. 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.