5 Two particles, of masses 3 kg and 7 kg , are connected by a light inextensible string that passes over a smooth peg. The 3 kg particle is held at ground level with the string above it taut and vertical. The 7 kg particle is at a height of 80 cm above ground level, as shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{5dd17095-18a6-470b-a24a-4456c8e3ed31-10_469_600_486_721} The 3 kg particle is then released from rest.

1. By forming two equations of motion, show that the magnitude of the acceleration of the particles is \(3.92 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
2. Find the speed of the 7 kg particle just before it hits the ground.
3. When the 7 kg particle hits the ground, the string becomes slack and in the subsequent motion the 3 kg particle does not hit the peg. Find the maximum height of the 3 kg particle above the ground.
   [0pt] [4 marks]