4. At time \(t = 0\) a ball is projected from a fixed point \(A\) on horizontal ground to hit a target. The ball is projected from \(A\) with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle \(\theta ^ { \circ }\) to the horizontal. At time \(t = 2 \mathrm {~s}\) the ball hits the target. At the instant when it hits the target, the ball is travelling downwards at \(30 ^ { \circ }\) below the horizontal with speed \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The ball is modelled as a particle moving freely under gravity and the target is modelled as the point \(T\).

1. Find
   1. the value of \(\theta\),
   2. the value of \(u\). The height of \(T\) above the ground is \(h\) metres.
2. Find the value of \(h\).
3. Find the length of time for which the ball is more than \(h\) metres above the ground during the flight from \(A\) to \(T\).