Edexcel M2 2008 June — Question 7

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2008
SessionJune
TopicProjectiles

7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a2738ce4-4dc5-4cd1-ac3d-0c3fcf21ea71-11_755_1073_246_287} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} A ball is thrown from a point \(A\) at a target, which is on horizontal ground. The point \(A\) is 12 m above the point \(O\) on the ground. The ball is thrown from \(A\) with speed \(25 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(30 ^ { \circ }\) below the horizontal. The ball is modelled as a particle and the target as a point \(T\). The distance \(O T\) is 15 m . The ball misses the target and hits the ground at the point \(B\), where \(O T B\) is a straight line, as shown in Figure 4. Find
  1. the time taken by the ball to travel from \(A\) to \(B\),
  2. the distance \(T B\). The point \(X\) is on the path of the ball vertically above \(T\).
  3. Find the speed of the ball at \(X\).