A carousel has three rings of wooden horses fixed to a circular platform, which rotates anticlockwise around a central pole. The inner ring of horses is 1.5 metres from the pole and the middle ring of horses is 2.4 metres from the pole. (Distances are between the centre of the pole and the centres of the horses.) Sisters Etsuko and Bachico sit on horses next to each other on the carousel.
The ride starts slowly but reaches a amximum speed during the first revolution. At the end of the first revolution, the siblings wave to their mother who is then directly alongisde them. The carousel continues to rotate at a maximum speed until they have passed their mother a further 16 times. The carousel then slows down and stops without the siblings passing their mother again. The time between the first and last time the siblings passed their mother was 6 minutes.
A) Etsuko sits on a horse on the inner ring. Calculate Etsuko's maximum speed in metres per second to 2 decimal places.
B) Bachico sits on a horse on the middle ring. Calculate hoy many times faster she is travelling compared to Etsuko.
C) The safety regulations for carousels state that the maximum speed at which it is safe for a child to sit on a horse without flying off is 1.5 metres per second. Find the maximum distance from the pole to the outer ring of horses to the nearest centimetre.
D) In the UK and Australia carousels are typically called merry-go-rounds and rotate clockwise. There is a merry-go-round near the carousel that Bachico and Etsuko are riding. Bachico's friend Sakura is riding the merry-go-round, which travels at 2 revolutions per minute. At certain times they were as close as possible, that is, simultaneously both on the imaginary straight line joining the two poles. Each time this happened they screamed 'yay'. Find the time in seconds between consecutive yays.
