ON YER BIKE!

A bicycle is being ridden in a straight line, when the rider does a U-turn and goes back in the direction he came from. He does this by suddenly turning her front wheel, holding the handlebars at a constant angle and then suddenly straightening the wheel again. 

Draw a sketch showing the tracks of the front and rear wheels during this manoeuvre, assuming that the bicycle stays vertical at all times and that the handlebars turn about a vertical axis. 

Calculate the distance between the initial and final wheel tracks, given that the distance between the cen-

tres of the wheels is one metre and the angle through which the front wheel is turned is 30◦.