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\includegraphics[max width=\textwidth, alt={}, center]{d0fa61eb-f320-427e-8883-de224d293933-3_515_789_995_676}
The diagram shows the vertical cross-section \(L M N\) of a fixed smooth surface. \(M\) is the lowest point of the cross-section. \(L\) is 2.45 m above the level of \(M\), and \(N\) is 1.2 m above the level of \(M\). A particle of mass 0.5 kg is released from rest at \(L\) and moves on the surface until it leaves it at \(N\). Find
- the greatest speed of the particle,
- the kinetic energy of the particle at \(N\).
The particle is now projected from \(N\), with speed \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), along the surface towards \(M\).
- Find the least value of \(v\) for which the particle will reach \(L\).