7.
\begin{figure}[h]
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\caption{Figure 3}
\includegraphics[alt={},max width=\textwidth]{19f831ad-5e32-470c-9974-beb82d5c9753-6_636_1617_406_184}
\end{figure}
A ball \(B\) of mass 0.4 kg is struck by a bat at a point \(O\) which is 1.2 m above horizontal ground. The unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are respectively horizontal and vertical. Immediately before being struck, \(B\) has velocity \(( - 20 \mathbf { i } + 4 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\). Immediately after being struck it has velocity \(( 15 \mathbf { i } + 16 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\).
After \(B\) has been struck, it moves freely under gravity and strikes the ground at the point \(A\), as shown in Fig. 3. The ball is modelled as a particle.
- Calculate the magnitude of the impulse exerted by the bat on \(B\).
- By using the principle of conservation of energy, or otherwise, find the speed of \(B\) when it reaches \(A\).
- Calculate the angle which the velocity of \(B\) makes with the ground when \(B\) reaches \(A\).
- State two additional physical factors which could be taken into account in a refinement of the model of the situation which would make it more realistic.