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]
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.
1 answer