3 A player projects a basketball with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle \(\theta\) above the horizontal. The basketball travels in a vertical plane through the point of projection and goes into the basket. During the motion, the horizontal and upward vertical displacements of the basketball from the point of projection are \(x\) metres and \(y\) metres respectively.
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1. Find an expression for \(y\) in terms of \(x , u , g\) and \(\tan \theta\).
2. The player projects the basketball with speed \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) from a point 0.5 metres vertically below and 5 metres horizontally from the basket.
   1. Show that the two possible values of \(\theta\) are approximately \(63.1 ^ { \circ }\) and \(32.6 ^ { \circ }\), correct to three significant figures.
   2. Given that the player projects the basketball at \(63.1 ^ { \circ }\) to the horizontal, find the direction of the motion of the basketball as it enters the basket. Give your answer to the nearest degree.
3. State a modelling assumption needed for answering parts (a) and (b) of this question.
   (1 mark)