Observation wheel seat height in a later revolution

A seat on an observation wheel is \(4\) metres above the ground at its lowest point at 10:00 am. It next reaches its lowest point at 10:16 am. The centre of the wheel is \(18\) metres above the ground.

Let \(t\) be the number of minutes after 10:00 am. The seat's height \(h(t)\), in metres, is modelled by \(h(t)=a\cos\bigl(b(t-c)\bigr)+18\), where \(a\), \(b\) and \(c\) are positive constants.

1. Determine \(a\) and \(b\).[4]
2. State the smallest positive value of \(c\).[1]
3. Find the first time after 10:25 am at which the seat is \(25\) metres above the ground. Give your answer to the nearest second.[4]