Double Ball Drop: Solve Elastic Collision Velocity Problem

[Gibanga]

Homework Statement

Hi everyone. Hope I'm not breaking any forum rules, because I've alread wrote this one in another thread by mistake. Here is where it should be.

Two balls of different mass are dropped one in top of the other, with the light one on top. After they collide with the floor (elastic collision), what is the velocity of both balls?

m is the mass of the small ball
M is the mass of the heavier one
v is the velocity of both balls before the collision with the ground
v1 and v2 are the velocities of the lighter and heavier ball respectively.

Homework Equations

p_i=p_f

The Attempt at a Solution

(m + M)v = mv₁ + Mv₂

What do i assume now?

I first assumed that mv₁ = -(m+M)v + Mv₂
but it doesn't look right to me because v₁ turns out 2v₂.

What am i doing wrong?

Thanks in advance.

 

[tiny-tim]

Welcome to PF!

Hi Gibanga! Welcome to PF!

… After they collide with the floor (elastic collision), what is the velocity of both balls?

Hint: https://www.physicsforums.com/library.php?do=view_item&itemid=38" means that energy is conserved.

 

[Gibanga]

Hi Gibanga! Welcome to PF!


Hint: https://www.physicsforums.com/library.php?do=view_item&itemid=38" means that energy is conserved.

Thank you very much.

Linear momentum is also conserved.

So i get two equations and two unknowns and a very ugly quadratic equation jumps out of there. Should i solve it or am i wasting my time? This looks like a very simple problem and I'm just making it more complex...