Moish, don't get worked up, not about the ticket or about the shmendy. it's obvious this shmendy knows nothing about the cops over in Israel which btw are not all jewish.
In regards to the ticket, assuming your in the MIR and located in Yerushalayim and asuming you didn't say anything stupid to the cop because they write on the ticket what you say. you need to wait at least 2 weeks from when you received the ticket and then you should go to "binyan clall" on yaffo street, i think it's the 9th floor it's the police dept. floor and take a number for disputing a ticket. when you get your turn be nice and ask them if they can switch it to a "azhara" a warning and dismiss the ticket, being that your from the states and you didn't know it was against the law and that you would chalila never break a law from the jewish state and that is your first ticket. they should throw it out. if you can't wait 2 weeks then you can go now and write a letter explaining the above and that should work too. make sure to bring the ticket with you. you can double check where their location is by calling the yerushalayim number on back of the ticket. Let me know what happens.
Also smart move that you had your contract with you otherwise they might of confiscated your car since they are ......