A bicycle wheel of diameter \(D=26\) inches \((1\) inch \(=2.54 \mathrm{~cm})\) is rotating with frequency \(f=1.0 \mathrm{~s}^{-1}\). Neglecting finite size and tire deformation, assuming the wheel as a circumference of diameter \(D\) and the tire valve as a point on the circumference:

1. determine the speed of the cyclist in motion on a straight road, assuming that the wheel rolls without crawling;
2. write the equation of motion of the valve for a stationary observer on the road. Assume that at \(t=0\) the valve is at position \((x, y)=(0, D)\) (axis \(X=\) straight road; axis \(Y=\) vertical);
3. determine (again for the observer stationary on the road) the velocity of the point (represented by the valve) when it is in contact with the ground.