The diameter of a car's tire is 60cm. While the car is being driven, the tire picks up a nail. At what times in two complete cycles is the nail at a height of 1cm above the ground.

Question

So far, I have calculated the circumference of the wheel (188.5) and I do not know the next step.

Answer 1

This is pretty "advanced" stuff
Your nail traces out a cycloid, the
equation of that path can be written as
parametric equations
x=r(t−sint)
y=r(1−cost) , where t is the angle of rotation, and r is the radius

What level of math is this ?

http://mathworld.wolfram.com/Cycloid.html

Answer 2

Grade 11 Unversity Functions.

The question was part of the final "Thinking" category for our periodic functions test.