A hurricane is heading from the Atlantic Ocean to Miami, Florida. If the centre of the hurricane goes within a 50 kilometre radius of the city centre, the city will sustain very severe damage.
A meteorologist models the city centre as a fixed particle located at the point (240 , 200). They then model the centre of the hurricane as travelling on a path relative to the city defined by \(y = kx + 20\).
The unit of distance for the meteorologist’s coordinate system is kilometres.
a) Find the values of k such that the city does not sustain severe damage.
b) State one limitation of the model.