5. Two particles \(P\) and \(Q\) have masses 2 kg and 5 kg respectively. The particles are connected by a light inextensible string which passes over a smooth, fixed pulley. Initially both \(P\) and \(Q\) are 2.1 m above horizontal ground. The particles are released from rest with the string taut and the hanging parts of the string vertical, as shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{6c69f370-0d2d-41ec-8761-0707a6ada43d-10_417_182_358_1032}
i. Show that the acceleration of \(Q\) as it descends is: \(4.2 \mathrm {~ms} ^ { - 2 }\)
ii. Find the tension in the string as \(Q\) descends.
iii. Explain how you have used the information that the string is inextensible and that the pulley is smooth. When \(Q\) hits the ground it does not rebound and the string becomes slack. Particle \(P\) then moves freely under gravity without reaching the pulley.
iv. Find the greatest height above the ground that \(P\) reaches.
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