In 1932, Giuseppe Momo was commissioned to build the famous Vatican Museum double spiral staircase. Suppose that it takes you one hour to slowly stroll at a constant speed up one spiral of this staircase, which has a radius of 19 feet and a height of 50 feet and makes 5 revolutions. (a) Assuming the spiral staircase is centered about the z-axis, find a vector function of the form (t) = (a cos(bt), a sin(bt), ct) for the helical path you take from the point (19, 0, 0) to the point (19, 0, 50) that makes 5 revolutions during the time interval 0 t 1. 7(1) = (b) How far did you walk? feet