You will have to use your imagination: 3 tracks are constructed as such... path 1 (P1) is similar to a "down-facing parabola," path 2 (P2) is straight, and path 3 (P3) is similar to an "up-facing parabola." P1 is "uphill," P2 is "through that hill," and P3 "under the hill, beneath P2, and exactly 'oposite' of P1." Okay! .... A mass m starting at point A (foot of the hill) is projected with the same initial horizontal velocity v along each of the three tracks (negligible friction) sufficient in each case to allow the mass to reach the end of the track at point B (oposite foot of the hill). The masses remain in contact with the tracks throughout their motions. The displacement A-B is the same in each case, and the total path length of P1 and P3 are the equal. If t1, t2, and t3 are the total travel times between A and B for P1, P2, and P3 respetively, what is the relation among these times? I said intuitively that: t2<t1=t3. correct?