A bicyclist is riding at 15 mph and her bike has wheels with a radius of 14 inches. She rides over a wad of gum which sticks in the tire. Assume this is t=0 seconds.
a.)Find a function that gives the height in inches above the ground of the gum, with the input in seconds.
Also give the period and the shift please. Thank you.
We know the function is sinusoidal because the gum is moving on the rim of a circle.
We need negative cosine because it is at ground level at t = 0.
We also need the time of one revolution:
(15mi/hr)(5280ft/mi)(1hr/3600s) = 264in/s
(264in/s)(1 rev/28Пin) = (66/7П)revolutions/sec
7П/66sec/rev
Hence the function is:
h = 14[ - (cos(132/7)t) + 1]