Drone height model and recording time

A drone is launched from a platform. Its height, \(h\) metres, above the ground \(t\) seconds after launch is modelled by \(h=-2t^2+16t+3\). Assume that the model is valid from launch until the drone reaches the ground.

1. By expressing \(h\) in the form \(a(t-p)^2+q\), find the greatest height of the drone and the time at which it occurs.[3]
2. A camera records the drone only while it is more than \(27\) m above the ground. Find the length of time for which the drone is recorded.[3]
3. The platform is changed so that the model becomes \(h=-2t^2+16t+c\), where \(c\) is a constant. The drone is now recorded for exactly \(5\) seconds. Find the value of \(c\) and check that your answer is consistent with the context.[4]