5. A particle is projected from a point with speed \(u\) at an angle of elevation \(\alpha\) above the horizontal and moves freely under gravity. When it has moved a horizontal distance \(x\), its height above the point of projection is \(y\).

1. Show that $$y = x \tan \alpha - \frac { g x ^ { 2 } } { 2 u ^ { 2 } } \left( 1 + \tan ^ { 2 } \alpha \right) .$$ A shot-putter puts a shot from a point \(A\) at a height of 2 m above horizontal ground. The shot is projected at an angle of elevation of \(45 ^ { \circ }\) with a speed of \(14 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). By modelling the shot as a particle moving freely under gravity,
2. find, to 3 significant figures, the horizontal distance of the shot from \(A\) when the shot hits the ground,
3. find, to 2 significant figures, the time taken by the shot in moving from \(A\) to reach the ground.