12 A girl is practising netball.
She throws the ball from a height of 1.5 m above horizontal ground and aims to get the ball through a hoop.
The hoop is 2.5 m vertically above the ground and is 6 m horizontally from the point of projection.
The situation is modelled as follows.
- The initial velocity of the ball has magnitude \(U \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
- The angle of projection is \(40 ^ { \circ }\).
- The ball is modelled as a particle.
- The hoop is modelled as a point.
This is shown on the diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{ec83c2c5-f8f8-4357-abfa-d40bc1d026b4-09_375_1207_1119_278}
- For \(U = 10\), find
- the greatest height above the ground reached by the ball
- the distance between the ball and the hoop when the ball is vertically above the hoop.
- Calculate the value of \(U\) which allows her to hit the hoop.
- How appropriate is this model for predicting the path of the ball when it is thrown by the girl?
- Suggest one improvement that might be made to this model.