# Elastic Momentum

#### Jordash

1. The problem statement, all variables and given/known data

Two elastic balls, one with mass m = 50 g and the other with mass M = 3m experience a head-on elastic collision after initially traveling in opposite directions at the same speed v = 15 m/s.

Use the conservation of momentum strategy to obtain symbolic expressions and numerical values
for the velocities of the two balls after the collision. (One of the answers is 3E1.)

2. Relevant equations

Mi1Vi1+Mi2Vi2=Mf1Vf1+Mf2Vf2

3. The attempt at a solution

Well I know that the initial Velocities are going to be the same so

M1+M2(Vi)=M1Vf1+M2Vf2

Would be correct

I'm not sure how you would solve this problem because you are looking for 2 unknowns?

Thanks for any help

#### Jordash

The Kinetic Energy is conserved

So I guess KEi=KEf

or

KEi=1/2M1Vi1^2+1/2M2Vi2^2
KEf=1/2M1Vf1^2+1/2M2Vf2^2

Where would I go from there?

Last edited:

#### LowlyPion

Homework Helper
Weren't you complaining about having 2 unknowns?

So don't you have 2 equations?

Homework Helper

#### Jordash

Ok, I used this equation:

Vi1+Vi2=Vf1+Vf2
Vi1-Vi2=Vf1-Vf2

which would mean

15m/s + -15m/s=Vf1+Vf2
0=Vf1+Vf2
or
Vf1=-Vf2

and

15m/s- -15m/s=Vf1-Vf2
15+15
30m/s=Vf1-Vf2

30m/s=Vf1-Vf1

what am I doing wrong?

#### LowlyPion

Homework Helper
One mass is 3 times the other.

#### Jordash

Oh yeah, good point

#### Jordash

I'm trying to take that into account but i'm still lost I think it's because I'm really rusty on Algebra

#### LowlyPion

Homework Helper
I'm trying to take that into account but i'm still lost I think it's because I'm really rusty on Algebra
Also try using the equations at the link I supplied.

Kinetic energy ... you know that ½mv² thing is also conserved.
Momentum is conserved.

Write them out carefully and solve..

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