I submitted this assignment and the teacher gave me 1/5 marks for this and I dont know why, she just said not enough information to prove the point. She NEVER tells you the solution even after she has marked the assignments so I feel pretty miserable because I dont know why my answer is not good enough. So I am asking here in hopes someone can help explain this to me.
The question is: A hiker leaves his cabin at 8 am and walks uphill to another cabin and reaches that cabin uphill at 8 pm. the next morning he leaves from his uphill cabin to go back to his downhill cabin. he leaves at 8 am and reaches the downhill cabin at 8 pm. prove that at one point in time the hiker was at the exact same spot when going uphill as he was downhill.
Now what I wrote for my solution was basically a graph of the hiker's journey, the graph looks kind of like $-x^2$'s graph. I said in order for him to make it to the cabin uphill or down hill, he must have maintained the same AVERAGE velocity. because the average velocity was the same for both trips, he must have reached one point at the exact same time on both trips.
she said not enough info and gave me 1/5..didnt even look at my beautiful graph or explanation