5.
\begin{figure}[h]
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\caption{Figure 1}
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Figure 1 represents the plan view of part of a horizontal floor, where \(A B\) and \(B C\) represent fixed vertical walls, with \(A B\) perpendicular to \(B C\).
A small ball is projected along the floor towards the wall \(A B\). Immediately before hitting the wall \(A B\) the ball is moving with speed \(v \mathrm {~ms} ^ { - 1 }\) at an angle \(\theta\) to \(A B\).
The ball hits the wall \(A B\) and then hits the wall \(B C\).
The coefficient of restitution between the ball and the wall \(A B\) is \(\frac { 1 } { 3 }\)
The coefficient of restitution between the ball and the wall \(B C\) is \(e\).
The floor and the walls are modelled as being smooth.
The ball is modelled as a particle.
The ball loses half of its kinetic energy in the impact with the wall \(A B\).
- Find the exact value of \(\cos \theta\).
The ball loses half of its remaining kinetic energy in the impact with the wall \(B C\).
- Find the exact value of \(e\).