I had a physics test last week. When I got the results, there were some correction mistakes in my opinion, so now it's being revised. I had a small disagreement with my professor over one of the theoric exercises, and tomorrow i'll probably be having the same argument again, so I thought of asking for some help with the concept of trajectory. (I don't have the test, but this is what I remember of the exercise) The main exercise was a simple problem in two dimensions in which a person threw a projectile from a certain height with initial velocity in the x axis, with some values given such as the distance travelled, time of flight of the particle, etc. One of the theoric points asked to find an equation that describes the trajectory of the projectile. What I tried to do was, having the equations that described movement in both axis, x(t) and y(t), somehow come up with an expression for y as a function of x, that would be y(x), but I couldn't do it. So instead I wrote this: x(t) y(t) with the correspondent equations for both, and then I wrote r(t)= (x(t), y(t)) And I marked this last function as the answer. Before I saw the correction I asked one of the assistants, who said: "y(x) does not describe the trajectory. This describes the trajectory (and he threw an object through the air)" That had not make sense to me, and when I saw the correction, i understood he was obviously wrong. The correction said that I did not find y(x), and it was marked wrong. The professor said to me: "If you'd marked y(t) and x(t) as the answers, it would've been OK too. But you marked the position as the answer" In my opinion, trajectory can be described in many ways, and the vector function r(t) that gives the position of the particle is one of them. Does r(t) describe the trajectory? Also, can r(t) be considered an equation?