11 A fire crew is tackling a grass fire on horizontal ground.
The crew directs a single jet of water which flows continuously from point \(A\).
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The path of the jet can be modelled by the equation
$$y = - 0.0125 x ^ { 2 } + 0.5 x - 2.55$$
where \(x\) metres is the horizontal distance of the jet from the fire truck at \(O\) and \(y\) metres is the height of the jet above the ground.
The coordinates of point \(A\) are ( \(a , 0\) )
11
- Find the value of \(a\).
11
- (ii) Find the horizontal distance from \(\boldsymbol { A }\) to the point where the jet hits the ground.
11 - Calculate the maximum vertical height reached by the jet.
11 - A vertical wall is located 11 metres horizontally from \(A\) in the direction of the jet. The height of the wall is 2.3 metres.
Using the model, determine whether the jet passes over the wall, stating any necessary modelling assumption.