7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{54642aff-2042-494e-ba4a-8332bd47a751-5_485_1191_194_333}
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\caption{Fig. 4}
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Figure 4 shows two golf balls \(P\) and \(Q\) being held at the top of planes inclined at \(30 ^ { \circ }\) and \(60 ^ { \circ }\) to the vertical respectively. Both planes slope down to a common hole at \(H\), which is 3 m vertically below \(P\) and \(Q\).
\(P\) is released from rest and travels down the line of greatest slope of the plane it is on which is assumed to be smooth.
- Find the acceleration of \(P\) down the slope.
- Show that the time taken for \(P\) to reach the hole is 0.904 seconds, correct to 3 significant figures.
\(Q\) travels down the line of greatest slope of the plane it is on which is rough. The coefficient of friction between \(Q\) and the plane is \(\mu\).
Given that the acceleration of \(Q\) down the slope is \(3 \mathrm {~ms} ^ { - 2 }\), - find, correct to 3 significant figures, the value of \(\mu\).
In order for the two balls to arrive at the hole at the same time, \(Q\) must be released \(t\) seconds before \(P\).
- Find the value of \(t\) correct to 2 decimal places.