4 A small ball \(B\) is projected with speed \(30 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(60 ^ { \circ }\) above the horizontal from a point \(O\). At time \(t \mathrm {~s}\) after projection the horizontal and vertically upwards 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 find the equation of the trajectory of the ball.
2. Find the value of \(x\) for which \(O B\) makes an angle of \(45 ^ { \circ }\) above the horizontal.