3. A ball of mass \(m\) is thrown vertically upwards from the ground. When its speed is \(v\) the magnitude of the air resistance is modelled as being \(m k v ^ { 2 }\), where \(k\) is a positive constant. The ball is projected with speed \(\sqrt { \frac { g } { k } }\).
By modelling the ball as a particle,
- find the greatest height reached by the ball.
- State one physical factor which is ignored in this model.