Dimensions and safety height of an underpass

Dimensions and safety height of an underpass

Secondary 2
4 marks
TGM Original Questions

Optional extension

The cross-section of an underpass is modelled by \(h=4.5-0.25x^2\), where \(h\) metres is the height and \(x\) metres is horizontal displacement from the centre.

  1. Find the full ground-level width.[2]
  2. For safety, vehicles may use at most 85% of the greatest height. Find this permitted height.[2]

Solution:

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Answer:(a) \(6\sqrt2\approx8.49\) m (b) \(3.825\) m.

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