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\includegraphics[max width=\textwidth, alt={}, center]{fd2fbf13-912c-46c5-a470-306b2269aa0b-3_378_1001_1672_573}
A particle \(A\) of mass 1.6 kg rests on a horizontal table and is attached to one end of a light inextensible string. The string passes over a small smooth pulley \(P\) fixed at the edge of the table. The other end of the string is attached to a particle \(B\) of mass 2.4 kg which hangs freely below the pulley. The system is released from rest with the string taut and with \(B\) at a height of 0.5 m above the ground, as shown in the diagram. In the subsequent motion \(A\) does not reach \(P\) before \(B\) reaches the ground.
- Given that the table is smooth, find the time taken by \(B\) to reach the ground.
- Given instead that the table is rough and that the coefficient of friction between \(A\) and the table is \(\frac { 3 } { 8 }\), find the total distance travelled by \(A\). You may assume that \(A\) does not reach the pulley.