Our hypothesis here is that sometimes when you do a physics calculation and you get two answers and you recognize one as being sensible…
…there might be something interesting about the “nonsense” answer.
A student does a calculation and gets a positive answer and a negative answer and says “we can’t go back in time, so of course the positive answer is correct!” The positive answer is correct, but…
HERE IS THE SETUP
Math is carefully done so a project launched at time zero will reach it high point in 3 seconds (at that point in time its velocity will be zero) and then it will fall and at t=6 seconds it hits the ground (at that point in time its position will be h=0).
Will all of this known to you and me, we ask a third person to come along and do the experiment starting their t=0 at what for us was t=4. we give them the velocity at t=4 (which is v=0 for them) and the height at t=4 (which is x_0 for them). They calculate that the object will hit the ground at time t=2.
Actually, they report that we have t=-4 or t=2. They say “but we can’t go back in time so obviously the answer has to be t=2.
We are kind and say “yes, t=2 is correct, we got that too. We just wanted someone else to confirm it.”
But you and I know that there is a reason why t=-4 appears as a solution. The object left the ground at a negative time (t=-4) according to their time, and that’s why the calculation is telling us that the object is at h=0 at both t=-4 and t=2.
Vectoreverything 