7.
\begin{figure}[h]
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\caption{Figure 3}
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\end{figure}
The object of a game is to throw a ball \(B\) from a point \(A\) to hit a target \(T\) which is placed at the top of a vertical pole, as shown in Figure 3. The point \(A\) is 1 m above horizontal ground and the height of the pole is 2 m . The pole is at a horizontal distance of 10 m from \(A\). The ball \(B\) is projected from \(A\) with a speed of \(11 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of elevation of \(30 ^ { \circ }\). The ball hits the pole at the point \(C\). The ball \(B\) and the target \(T\) are modelled as particles.
- Calculate, to 2 decimal places, the time taken for \(B\) to move from \(A\) to \(C\).
- Show that \(C\) is approximately 0.63 m below \(T\).
(4)
The ball is thrown again from \(A\). The speed of projection of \(B\) is increased to \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the angle of elevation remaining \(30 ^ { \circ }\). This time \(B\) hits \(T\). - Calculate the value of \(V\).
(6) - Explain why, in practice, a range of values of \(V\) would result in \(B\) hitting the target.