The diagram shows two particles \(A\) and \(B\), connected by a light inextensible string which passes over a smooth fixed peg. The system is held with the string taut and with \(A\) and \(B\) each at a height of \(\quantity{0.09}{m}\) above a fixed horizontal plane; it is then released from rest. When \(B\) reaches the plane is becomes stationary.

Calculate

the tension in the string while both particles are in motion,

the speed of the particles when \(B\) reaches the plane,

the maximum height above the plane attained by \(A\), assuming that \(A\) does not reach the height of the fixed peg.

[Take \(g\) to be \(\quantity{10}{m\,s^{-2}}\).]