Answer

It is not “his arrows,” because there is no direct force here. Simply speaking, it is either “foot” or a moving pit, and in practice it is a covered pit (since it has mechanisms that prevent accidents). Therefore it should be treated like a car with a regular driver. If the injured party could have protected himself, then it is his fault and the damager is exempt. And if not, he is liable as with a moving pit. Also under the category of “foot,” the exemption in the public domain is only because you have the right to move it there, and the duty to protect oneself falls on the injured party (as written by the Rif, Maimonides, and others). Therefore, if he could not have protected himself, the damager is liable.