The diameter of a car's tire is 5oem. While the car is being driven, the tire picks up a nail. It takes 1 second for the nail to rotate to the top of the tire.
a) Graphically model the height of the nail above the ground over time, from the point it punctures the
tire. Include 3 rotations of the tire in your model.
b) Algebraically model the path of the nail in terms of sine and cosine.
c) How high above the ground is the nail after 6.35 second?
d) At what time(s) in the first 3 rotations of the tire is the nail 13cm above the ground?
e) If the car drives for 6 minutes, how many times will the nail have rotated around the tire?
f) State the domain and range of the path of the nail.
g) What assumptions must you make about the drive in order for the function to accurately model the
nails path?

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