Representing the arch as an inverted parabola with general equation y=-ax2+b where a and b are positive constants, the vertex is at (0,b)=(0,45), making y the axis of symmetry. The x-intercepts are, by symmetry, at (-90,0) and (90,0).
y=-ax2+45, 0=-8100a+45, so a=45/8100=1/180 and y=45-x2/180.
The boat is at x=±30, x2=900; y=45-900/180=40 feet, so the 30ft-tall boat has 10ft of clearance above it and should pass safely under the bridge.