Edexcel M1 2024 January — Question 4

Exam BoardEdexcel
ModuleM1 (Mechanics 1)
Year2024
SessionJanuary
TopicVectors Introduction & 2D

4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e59a66b8-c2ad-41fd-9959-9d21e9455c37-08_399_889_246_587} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Figure 3 shows two horizontal forces \(\mathbf { P }\) and \(\mathbf { Q }\) acting on a particle.
The angle between the direction of \(\mathbf { P }\) and the direction of \(\mathbf { Q }\) is \(150 ^ { \circ }\)
Force \(\mathbf { P }\) has magnitude \(X\) newtons.
Force \(\mathbf { Q }\) has magnitude \(5 \sqrt { 3 } \mathrm {~N}\).
The resultant of \(\mathbf { P }\) and \(\mathbf { Q }\) has magnitude \(\sqrt { 129 } \mathrm {~N}\).
Find
  1. the value of \(X\).
  2. the angle between \(\mathbf { Q }\) and the resultant, giving your answer to the nearest degree.