Listen, I have this from all angles. I was a teenager your age. I had parents, just like you do. I grew up and became a mother, so I have raised teenagers. Trust me, I got this one from every possible scenario because I have been a player as a child with parents, the child, the parent, the parent with children. Gosh, I hate to sound like my mother here, but as such, your mother is right. She is.
I had the same situation with my son who wanted to travel from the east coast to Colorado to meet an internet friend. I forbade him to go. But, when he turned 18, he had his own money, bought an air line ticket and went. I was a nervous wreck and could not eat or sleep well for 4 days. And, that was after he had known her through the internet since they were 13 years old. I "met" her and her mother through an internet camera. I did research on line to find that these people really existed. I did a google map search to see if the house was really there. I used their local town hall web site to be sure they were who they said they were and lived where they said they lived. But, even still, I was scared out of my witts when he left for that trip. I made him call me every step of the way there and back. I am not a paranoid person, at all, but I was so on edge that my kid was traveling alone.
I was an invincible teenager once. But that was a time when life was very different than it is today. Today there are organized criminals who trick solo travelers and kidnap them to be used as sex slaves. I know this sounds so far fetched to you, but it happens every single day, all over the world. These criminals are super organized and place themselves in bus stations, airports and train stations, LOOKING for women traveling alone. They are taxi cab drivers, they are young guys pretending to be friendly travelers and they are so good at what they do that you do not realize it is happening until it is too late. Please watch "Taken", a movie about these matters. It is astounding that this is happening all over the world.
I am not suggesting your friend is involved in any criminal activity. It is traveling there, being there and getting back home that is so very risky. I was your age once and I disobeyed my parents by smoking pot, drinking and being with boys, staying out later than I should and such. I was lucky to have survived without a scratch. I did have a schoolmate that got drunk and was with a guy who took sexual advantage of her and when she fought back, he beat her up and dumped her into a lake and took off, thinking she was dead. The water revived her and she managed to get to shore and crawled on her hands and knees, beaten and naked in the wee morning hours until she found a house to get some help. That bastard who hurt her is still in jail.
Do not travel alone. Go with another friend or have her travel to you with one of her friends. Your mother is not being unreasonable. You just do not realize that you are at the perfect time of your life to be taken advantage of and putting yourself at risk is frightening to a parent.