A ball thrown from a viewing platform

A small ball is thrown vertically upwards from the edge of a viewing platform. Its height \(h\) metres above horizontal ground, \(t\) seconds after release, is modelled by \(h=-5t^2+20t+25\). The model applies from release until the ball first reaches the ground. Air resistance is ignored.

1. State the height above the ground from which the ball is released.[1]
2. Express \(h\) in the form \(A-B(t-C)^2\), where \(A\), \(B\) and \(C\) are constants. Hence find the maximum height of the ball and the time at which it occurs.[4]
3. Find the time taken for the ball to reach the ground.[3]
4. Find the two times when the ball is \(40\text{ m}\) above the ground, and the time interval between these two instants.[3]