I apologize if this question has been asked before, but I haven't been able to find a post which covers this exact question.
Let's say that we have a driving car which is moving forward. At some point, one of the rotating tires hit a stone on the road. Which way does the stone move, in relationship with the angle in which the tire hits the stone? Can the stone ever be thrown backward onto another car?
Does the general direction (forward, backward, sideways) depend furthermore on the shape of the stone? Whether it is for example perfectly spherical or asymmetric?
I am kind of struggling how I would answer such a basic question, since there seems to be many factors at play here. Can you even answer this question without fully knowing all the nuances and details?
Suppose a rock is lodged in the tread of the tire.
$x=v_xt + R\cos(\omega t)$
$z=R \sin (\omega t)$
$dx/dt =v_x-\omega R\cos(\omega t)$
Typically, $v_x=\omega R$
So it generally wouldn't go backward, but can be overtaken by a car behind it effectively having the same result.
This implies $dx/dt = 2v_x\sin^2(\omega t/2) \implies dx/dt> 0$
This changes if $v\ne \omega R$, but that's the primary effect.