# What is the final velocity of mass

1. Nov 16, 2008

### Inertialforce

1. The problem statement, all variables and given/known data
A ball of mass 20.0kg (mass A) traveling at a initial speed of 5.0m/s, collides with a ball of mass 10.0kg (mass B) which was traveling at a initial speed of 1.0m/s. What is the final velocity of mass A, what is the final velocity of mass B?

mA = 2mB

2. Relevant equations
ΣFext = 0
Δp = 0
ΔEk = 0

3. The attempt at a solution
I am unsure how to find the final velocities here because I have two variables and I have to use the quadratic equation to find the final velocities right? So I was just wondering if I could somehow isolate and get rid of a variable, this is what I have so far:

Δp=0
PiA + PiB = PfA +PfB
mAviA + mBviB = mAvfA + mBvfB
mAviA + 2mAviB = mAvfA + 2mBvfB
viA + ViB = vfA + vfB
(5.0) + (1.0) vfA + vfB
6.0-vfA = vfB

Then I put it into the kinetic energy equation and put in all the numbers and I got as an answer:

510.0 = (20.0)(vfA)(squared) + (10.0)(vfB)(squared)

My question is basically how am I supposed to incorporate this into the quadratic equation to find the final velocities?

2. Nov 16, 2008

### fluidistic

Re: Momentum

I'm not sure about what I will say but I think I'm right. It is an elastic collision.
From the point of view of the mass B, the mass A collides at $$\frac{4m}{s}$$ and the mass B is at rest.
So the problem remains simple. $$m_Av_A=m_Bv_{Bf} \Leftrightarrow v_{Bf}=\frac{m_Av_A}{m_B}=\frac{20kg\cdot 4m}{10kg\cdot s}$$.
I'm not 100% sure though.