# #1 An Advanced but Simple Motion-in-1D Problem (1)

I get these physics problems from Engineering Physics Course at my recent university, Bandung Institute of Technology, Indonesia. The questions are really simple but needs an advance and deep analysis to answer them. The system of answering the science problems here in my university is quite unique: there are more than 1 correct answer (e.g. 2 correct answers) if 2 students have a different but reasonable justification and analysis of the problem. It depends on your analysis, not the correct answer. One vivid example, 1+1 has two correct answers, which are 2 based on ordinary arithmetic calculation and 1 based on Boolean algebra. I'm about to regularly give some of the problems here and consult them here. Let's see the problem here:

A particle is thrown away with degree elevation of α above the earth surface. Whenever the particle will undergo motion which is going farther from the initial point if and only if the vector components of its rate of motion are parallel to the vector components of its vector of position. Let g be the earth’s gravitational acceleration. What will be the value of α in order for the particle to always undergo motion which is always going farther from the initial point?

My friend and I have 2 different answers. I answer tan α = (y+1/2gt2 / x) based on parabollic motion. I assume parabollic motion as an approach because every time, the particle will always go farther from the initial point with degree elevation α. It won't be vertical motion because at the minimum point, the particle will go down again and go back to its initial point. Thus, I use parabollic motion formulas to find α with y, g, and x variable. On the other hand, my friend answers sin α > sqrt(8/9) based on his vector analysis which I don't understand *haha lol*.