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Q6. a) A keyway, of width 28mm, is cut into a stainless - steel shaft of diameter 100mm, as shown in FigQ6(a).

Calculate the shortest distance from the centre of the shaft A to the keyway. (8)

(b) The depth of water, h metres, over a bar at the entrance to a harbor on a particular day is given by h = 3 + 2 cos⁡ πt/6 where t is the number of hours after local high - water.

Determine EACH of the following for the day:

(i) the minimum depth of water over the bar; (2)

(ii) the time when the minimum depth occurs; (3)

(iii) the latest time after high - water when fishing vessel of draught 2.6 metres may leave the harbour with a clearance of 1 metre over the bar. (3)