1 A golf ball is hit at an angle of \(60 ^ { \circ }\) to the horizontal from a point, O, on level horizontal ground. Its initial speed is \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The standard projectile model, in which air resistance is neglected, is used to describe the subsequent motion of the golf ball. At time \(t \mathrm {~s}\) the horizontal and vertical components of its displacement from O are denoted by \(x \mathrm {~m}\) and \(y \mathrm {~m}\).

1. Write down equations for \(x\) and \(y\) in terms of \(t\).
2. Hence show that the equation of the trajectory is $$y = \sqrt { 3 } x - 0.049 x ^ { 2 }$$
3. Find the range of the golf ball.
4. A bird is hovering at position \(( 20,16 )\). Find whether the golf ball passes above it, passes below it or hits it.