7 A particle is projected with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(\theta\) above the horizontal from a point \(O\). At time \(t \mathrm {~s}\) after projection, the horizontal and vertically upwards displacements of the particle from \(O\) are \(x \mathrm {~m}\) and \(y \mathrm {~m}\) respectively.

1. Express \(x\) and \(y\) in terms of \(t\) and \(\theta\) and hence obtain the equation of trajectory $$y = x \tan \theta - \frac { g x ^ { 2 } \sec ^ { 2 } \theta } { 2 u ^ { 2 } } .$$ In a shot put competition, a shot is thrown from a height of 2.1 m above horizontal ground. It has initial velocity of \(14 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(\theta\) above the horizontal. The shot travels a horizontal distance of 22 m before hitting the ground.
2. Show that \(12.1 \tan ^ { 2 } \theta - 22 \tan \theta + 10 = 0\), and find the value of \(\theta\).
3. Find the time of flight of the shot.