Rail cars travellind down to a mine have to pass through the tunnel entrance show. The tunnel entrance is in the form of a semi-elliptical arch 6 metres wide and 4 metres tall. Each rail car is 4 metres wide and passes through the middle of the tunnel. The rail cars have a rectangular cross-section and come in three types with three differnt heights as show in the table.
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rail car height
The alpha 2m
The beta 2.5m
the gamma 3.2m
Which of these types of rail car will pass safely through the tunnel entrance?
Write down the semi-ellipse as a formula and then determine how high it is at the points 2m from the middle.