1 A small ball is projected with speed \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(45 ^ { \circ }\) above the horizontal from a point \(O\) on horizontal ground. At time \(t \mathrm {~s}\) after projection, the horizontal and vertically upwards displacements of the ball from \(O\) are \(x \mathrm {~m}\) and \(y \mathrm {~m}\) respectively.

1. Express \(x\) and \(y\) in terms of \(t\).
2. Show that the equation of the trajectory of the ball is \(y = x - \frac { 1 } { 40 } x ^ { 2 }\).
3. State the distance from \(O\) of the point at which the ball first strikes the ground.