1. The problem statement, all variables and given/known data Please see the attached photo. (down) Hminitial= 1.5R M = 2/3m Perfectly elastic collision What is the velocity of object m immidiatly after the collision? (by m,g,R) 2. Relevant equations Conservation of energy Conservation of momentum 3. The attempt at a solution I assumed that because of the elastic collision the M object bounce back, so I considered positive velocity to the right and negative to the left (when we're looking exactly on the collision moments) First I found the "before the collision" velocity of the falling ball M (with conservation of energy) which is √(3Rg) Now I used two equation to find the velocities after the collision : Conservation of momentum: MVi + 0 = MVf +mvf Conservation of energy: V0 + Vf = v0 + vf After some work I get : Vf = ⅓⋅√(3Rg) vf = 4⋅√(3Rg) / 3 It seems make sense when the speed of the small ball got higher and the big ball, which bounced backward, slower . But in the other hand I know that the M velocity after the collision has to be negative. because it bounced back!, perfectly elastic collision.... But I got 2 positive answers! when I try to change the direction/sign (to minus) of the variable MVf on the first equation I get different and not logical answer (Vf = √(3Rg) ) , like the bigger ball didn't lost energy at all while it was giving energy to the smaller ball... Please some help :) Thanks.