A man is standing 14 m away from the centre of a spinning wheel that is 4 m off the ground, spins at 4 rotations a second and has a diameter of 3 m. If the man is 1.5 m tall, how close does his head get from any part of the wheel?

Answer 1

You leave a lot unsaid, but if the wheel is on a vertical axis, then the distance from the man's head to the closest part of the wheel is
√(14-1.5)^2 + (4-1.5)^2) = 12.7 m
the distance to the farthest spot on the wheel would be
√((14+1.5)^2 + (4-1.5)^2) = 15.7 m

the speed of the wheel is irrelevant.