# Two body final velocities (check this please)

1. Jul 4, 2014

### dean barry

1. The problem statement, all variables and given/known data
Two masses m1 & m2 in free space are released from rest at a distance D and draw together under gravity to a distance d, calculate the final velocity of each mass.

2. Relevant equations
Final total KE of both bodies at d from :
KE (t) = ( ( G * m1 * m2 ) / d ) - ( ( G * m1 * m2 ) / D )
(Joules)

3. The attempt at a solution
Split the KE (t) by mass ratio, so :
KE (m1) = ( m2 / ( m1 + m2 ) ) * KE (t)
KE (m2) = ( m1 / ( m1 + m2 ) ) * KE (t)

The final velocities from :
v (m1) = sqrt ( ( KE ( m1 ) ) / ( ½ * m1 ) )
v (m2) = sqrt ( ( KE ( m2 ) ) / ( ½ * m2 ) )

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

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jul 4, 2014

### sankalpmittal

Ratio of kinetic energies of two particles is NOT the same as ratio of their masses.

Use following laws:

1. Conservation of linear momentum
2. Conservation of mechanical energy.

CONCEPT of LOST MASS might also be useful.