7 A small ball \(B\) is projected with speed \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(41 ^ { \circ }\) above the horizontal from a point \(O\) which is 1.6 m above horizontal ground. At time \(t \mathrm {~s}\) after projection the horizontal and vertically upward displacements of \(B\) from \(O\) are \(x \mathrm {~m}\) and \(y \mathrm {~m}\) respectively.

1. Express \(x\) and \(y\) in terms of \(t\) and hence show that the equation of the trajectory of \(B\) is $$y = 0.869 x - 0.0390 x ^ { 2 }$$ where the coefficients are correct to 3 significant figures. A vertical fence is 1.5 m from \(O\) and perpendicular to the plane in which \(B\) moves. \(B\) just passes over the fence and subsequently strikes the ground at the point \(A\).
2. Calculate the height of the fence, and the distance from the fence to \(A\).