6. A small package \(P\), of mass 1 kg , is initially at rest on the rough horizontal top surface of a wooden packing case which is 1.5 m long and 1 m high and stands on a horizontal floor. The coefficient of friction between \(P\) and the case is 0.2 .
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\(P\) is attached by a light inextensible string, which passes over a smooth fixed pulley, to a weight \(Q\) of mass \(M \mathrm {~kg}\) which rests against the smooth vertical side of the case.
The system is released from rest with \(P 0.75 \mathrm {~m}\) from the pulley and \(Q 0.5 \mathrm {~m}\) from the pulley. \(P\) and \(Q\) start to move with acceleration \(0.4 \mathrm {~ms} ^ { - 2 }\). Calculate

1. the tension in the string, in N ,
2. the value of \(M\),
3. the time taken for \(Q\) to hit the floor. Given that \(Q\) does not rebound from the floor,
4. calculate the distance of \(P\) from the pulley when it comes to rest.