2025 AISS PRELIMS P1 Q11

The horizontal distance of a child on a carousel, \(h\) m, from the starting point is modelled by the equation, \(h=2(1-\cos kt)\), where \(k\) is a constant and \(t\) is the time in seconds after the child leaves the starting point. The time to complete one revolution is 20 seconds.

1. Explain why this model suggests that the diameter of the carousel is 4 m.[1]
2. Show that the value of \(k\) is \(\frac{\pi}{10}\) radians per second.[2]
3. As the carousel turns, it is possible for the child on the carousel to view a landmark, provided that the horizontal distance of the child is within 1 m from the starting point. Find the duration of time for which the child will not be able to view the landmark during one revolution.[5]