Question

If the hula hoop is positioned vertically on the floor so that the black band is touching the floor, when the hula hoop is given a push, it begins to travel upright along the floor. The path traced out by the black band is given by the position vector r= (t – sin t) i + (1 – cos t) j. a) Graph the vector function that represents the path traced out by the black band either with a graphing utility or sketch it by hand. Make certain to include your Window settings and provide justification for your setting selections. b) What are the vector functions that represent the velocity and acceleration? c) Find the maximum and minimum values of the velocity vector analytically. d) Find the maximum and minimum values of the acceleration vector analytically. e) Provide a graphical representation of the velocity and acceleration vectors. Do they confirm your answers to c and d?

Answer 1

Solution: