A fountain jet and a screen

A fountain nozzle at the surface of a pool sends a narrow jet of water along a parabolic path. The water returns to the surface \(6\text{ m}\) horizontally from the nozzle. Its greatest height above the water surface is \(2.7\text{ m}\).

The path is modelled by \(h=ax(6-x)\) for \(0\leq x\leq6\), where \(x\) metres is the horizontal distance from the nozzle and \(h\) metres is the height above the water surface.

1. Find the value of \(a\).[2]
2. Find the two horizontal distances from the nozzle at which the jet is \(2.4\text{ m}\) above the water surface.[3]
3. A thin vertical screen is placed \(5\text{ m}\) horizontally from the nozzle. Its top is \(1.2\text{ m}\) above the water surface. Determine whether the jet passes at least \(0.2\text{ m}\) above the screen.[3]
4. State one assumption, other than the parabolic model, needed to use your result in (c) in practice.[1]