7. (5 marks). An ant is sitting on the rim of a bike wheel suspended 0.5ft in the air (thecircle shown below is meant to symbolize the bike wheel).

The ant is initially at the point P on the wheel, but the wheel is spun at a constant speed so that it moves around in circles counterclockwise, making 1 full revolution each minute. As a result, the ant's height as a function of time t (measured in minutes) can be modelled using an equation of the form h(t)=A+B \sin (2 \pi t)+C \cos (2 \pi t) (1 mark). Identify the times during the first minute of spinning at which the antis at the points P, Q, R and S. ) (1 mark). Given that the bike wheel has a radius of 1ft, identify the heights of the points Q, R and S. Then use this and your answer to (a) to find the values of A, B and C so that h(t) models the ant's height for all t. . Find the rate of change of the ant's height (i.e. the ant's vertical velocity ) (1 mark). At what time(s) (in the first minute) is the ant's vertical velocity 0?Does your answer make sense based on the picture?