10.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{65e4b254-fb7b-45c2-9702-32f034018193-32_435_1257_244_402}
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\caption{Figure 4}
\end{figure}
A boy throws a ball at a target. At the instant when the ball leaves the boy's hand at the point \(A\), the ball is 2 m above horizontal ground and is moving with speed \(U\) at an angle \(\alpha\) above the horizontal.
In the subsequent motion, the highest point reached by the ball is 3 m above the ground. The target is modelled as being the point \(T\), as shown in Figure 4.
The ball is modelled as a particle moving freely under gravity.
Using the model,
- show that \(U ^ { 2 } = \frac { 2 g } { \sin ^ { 2 } \alpha }\).
The point \(T\) is at a horizontal distance of 20 m from \(A\) and is at a height of 0.75 m above the ground. The ball reaches \(T\) without hitting the ground.
- Find the size of the angle \(\alpha\)
- State one limitation of the model that could affect your answer to part (b).
- Find the time taken for the ball to travel from \(A\) to \(T\).