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.

Answer 1

a) The parametric curve for the vector will be

1 LO -5 0

sin(t), y(t)1- cos(t) r(t)t cOS

Since the curve -1 < sin(t) < 1 and -1 < cos(t) < 1

Hence the value of y varies from [0,2]

whereas the value of x(t) varies from [t-1,t+1]

Hence we have selected the window for x being [-10,10] and y being [-5,5]

Note - Post any doubts/queries in comments section.