At what speed should the car go so that the pebble stuck in the tire that fell off its wheel at point A

At what speed should the car go so that the pebble stuck in the tire that fell off its wheel at point A would hit the same point on the wheel from which it came off? Wheel radius 20 cm.

It is natural to solve the problem in the frame of reference associated with
by a car, where the points of the wheel rim move in a circle with a speed v. In this system, the pebble will begin to move vertically upwards at exactly this speed. For the full time of its flight t = 2v / g, the wheel must complete an integer N number of revolutions, i.e. t = N * (2п * R) / V.
Hence V = √ (N * п * g * R) = 2.5 * √N.

There are quite a few suitable speed values.
Even with N = 100, we get a very real value of the speed (about 90 tkm / h).

Answer: V = √ (N * п * g * R).

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