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.

Question

anonymous · Answer

rail car           height
The alpha          2m
The beta            2.5m
the gamma           3.2m

anonymous · Answer

Which of these types of rail car will pass safely through the tunnel entrance?

nowhereman · Answer

Write down the semi-ellipse as a formula and then determine how high it is at the points 2m from the middle.