# New velocity between two spacecraft moving in opposing directions

1. Oct 10, 2011

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

A 60-tonne (1 t = 1000 kg) spacecraft moving in the + x-direction at 0.70 m/s docks with a 65-tonne craft moving in the -x-direction at 0.64 m/s

Find the velocity of the joined spacecraft

2. Relevant equations

Conservationg of kinetic energy?

KE_i=KE_f
3. The attempt at a solution

I don't know if this is silly, but I tried solving for the velocity using kinetic energies of the seperate space ships equalling the joined space ships:

1/2mv_1^2+1/2mv_2^2=1/2mv_3^2
1/2(60000kg)(0.70m/s)^2+1/2(65000kg)(0.64m/s)^2=(125000)v_3^2
14700+13312=62500v_3^2
v_3^2=0.4482
v_3=0.6695m/s

2. Oct 10, 2011

### lightgrav

Which direction do you think that velocity would be?

no, they "lock them together" before they can bounce apart.
what's conserved here is total momentum (vector).

3. Oct 10, 2011

Okay, so I can use P=mv for each respective part?

4. Oct 10, 2011

The velocity would be in the direction the heavier ship is going

5. Oct 10, 2011

### lightgrav

the heavier ship isn't going as fast ... just add them up, being careful with +/- signs.

6. Oct 10, 2011

Okay so the lighter ship is going faster but the larger ship is going slower, I don't understand what equation im supposed to use to find the velocity of the combined*

7. Oct 10, 2011

### lightgrav

you compute each one's momentum, then you add them.

Total momentum is the same after connecting as it was before connecting.

8. Oct 10, 2011