7 The points \(O\) and \(P\) are on a horizontal plane, a distance 8 m apart. A ball is thrown from \(O\) with speed \(u \mathrm {~ms} ^ { - 1 }\) at an angle \(\theta\) above the horizontal, where \(\tan \theta = \frac { 4 } { 3 }\). At the same instant, a model aircraft is launched with speed \(5 \mathrm {~ms} ^ { - 1 }\) parallel to the horizontal plane from a point 4 m vertically above \(P\). The model aircraft moves in the same vertical plane as the ball and in the same horizontal direction as the ball. The model aircraft moves horizontally with a constant speed of \(5 \mathrm {~ms} ^ { - 1 }\). After \(T \mathrm {~s}\), the ball and the model aircraft collide.
- Find the value of \(T\).
- Find the direction in which the ball is moving immediately before the collision.
If you use the following page to complete the answer to any question, the question number must be clearly shown.