Wednesday, July 13, 2011

Periodic modelling problem solving, need help?

On a particular day in harbour, the periodic cycle of the tide is 12 hours. The average depth of the water in the harbour is 4.5m. This depth rises 3.5m and falls 3.5 m at high and low tides respectively and the first high tide of the day occurs at 2 am. A ship requires that there is at least 7 m of water in order to safely enter and leave the harbour. Find a sinusoidal function that models the depth, f (t), of the water in the harbour t hours after midnight and hence find the times of day when the ship can safely enter and leave the harbour.

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