5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{414946db-64d7-44b8-801d-2c7805ee9cc6-16_303_1266_237_404}
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\caption{Figure 3}
\end{figure}
A golf ball is at rest at the point \(A\) on horizontal ground.
The ball is hit and initially moves at an angle \(\alpha\) to the ground.
The ball first hits the ground at the point \(B\), where \(A B = 120 \mathrm {~m}\), as shown in Figure 3.
The motion of the ball is modelled as that of a particle, moving freely under gravity, whose initial speed is \(U \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
Using this model,
- show that \(U ^ { 2 } \sin \alpha \cos \alpha = 588\)
The ball reaches a maximum height of 10 m above the ground.
- Show that \(U ^ { 2 } = 1960\)
In a refinement to the model, the effect of air resistance is included.
The motion of the ball, from \(A\) to \(B\), is now modelled as that of a particle whose initial speed is \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
This refined model is used to calculate a value for \(V\) - State which is greater, \(U\) or \(V\), giving a reason for your answer.
- State one further refinement to the model that would make the model more realistic.