2 A ball is kicked from ground level over horizontal ground. It leaves the ground at a speed of 25 ms 1 and at an angle \(\theta\) to the horizontal such that \(\cos \theta = 0.96\) and \(\sin \theta = 0.28\).

1. Show that the height, \(y \mathrm {~m}\), of the ball above the ground \(t\) seconds after projection is given by \(y = 7 t - 4.9 t ^ { 2 }\). Show also that the horizontal distance, \(x \mathrm {~m}\), travelled by this time is given by \(x = 24 t\).
2. Calculate the maximum height reached by the ball.
3. Calculate the times at which the ball is at half its maximum height. Find the horizontal distance travelled by the ball between these times.
4. Determine the following when \(t = 1.25\).
   (A) The vertical component of the velocity of the ball.
   (B) Whether the ball is rising or falling. (You should give a reason for your answer.)
   (C) The speed of the ball.
5. Show that the equation of the trajectory of the ball is $$y = \frac { 0.7 x } { 576 } ( 240 - 7 x )$$ Hence, or otherwise, find the range of the ball.