7. An ant is sitting on the rim of a bike wheel suspended 0.5ft in the air (the crcle shown below is meant to symbolize the bike wheel). R 0.5ft The ant is initially at the point P on the wheel, but...

Extracted text: 7. An ant is sitting on the rim of a bike wheel suspended 0.5ft in the air (the crcle shown below is meant to symbolize the bike wheel). R 0.5ft 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(2at) + C'cos(2nt). 'Identify the times during the first minute of spinning at which the ant (a) at, the points P, Q, R and S. (b) . Given that the bike wheel has a radius of lft, 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. (c) s). Find the rate of change of the ant's height (i.e. the ant's vertical velocity). (d) Does your answer make sense based on the picture? At what time(s) (in the first minute) is the ant's vertical velocity 0?