7 A smooth track \(A B\) is in the shape of an arc of a circle with centre \(O\) and radius 1.4 m . The track is fixed in a vertical plane with \(A\) above the level of \(B\) and a point \(C\) on the track vertically below \(O\). Angle \(A O C\) is \(60 ^ { \circ }\) and angle \(C O B\) is \(30 ^ { \circ }\). Point \(C\) is 2.5 m vertically above the point \(F\), which lies in a horizontal plane. A particle of mass 0.4 kg is placed at \(A\) and projected down the track with an initial velocity of \(0.8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The particle first hits the plane at point \(H\) (see diagram).
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1. Find the magnitude of the contact force between the particle and the track when the particle is at \(B\). [5]
2. Find the distance \(F H\).