A traffic tunnel is being planned. This diagram shows the cross-section of the tunnel. The shape of the tunnel is the same as the graph of $y=\frac49(9-x^2)$. All distances are in metres.
Which of these vehicles will fit through the tunnel?
a) truck, 2.9 m high, 4 m wide
b) coach, 3.4 m high, 3 m wide
c) lorry, 3.9 m high, 2 m wide
This problem is adapted from the World Mathematics Championships