11 In this question you must show detailed reasoning.
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A football \(P\) is kicked with speed \(25 \mathrm {~ms} ^ { - 1 }\) at an angle of elevation \(\alpha\) from a point \(A\) on horizontal ground. At the same instant a second football \(Q\) is kicked with speed \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of elevation \(2 \alpha\) from a point \(B\) on the same horizontal ground, where \(A B = 72 \mathrm {~m}\). The footballs are modelled as particles moving freely under gravity in the same vertical plane and they collide with each other at the point \(C\) (see diagram).
- Calculate the height of \(C\) above the ground.
- Find the direction of motion of \(P\) at the moment of impact.
- Suggest one improvement that could be made to the model.
\section*{OCR}
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