This *feels* right to me:

But I am having a little trouble with the mathematics.

**Two spaceships, A and B, with mass 1, velocity 10 and -10, collide head on.**

*Before collision:*

```
KE = 0.5 * mass * velocity^2
**Spaceship A**
KE = 0.5 * 1 * 10^2
KE = 50
**Spaceship B**
KE = 0.5 * 1 * 10^2
KE = 50
```

*After collision:*

If the spaceships were non-deformable to preserve momentum and energy they would perfectly bounce off each other like billiard balls? Correct?

Assuming they deform and “stick” together, for momentum to be conserved (which was previously (10*1) + (-10*1) = 0) they must come to a stop. For the 50 KE per spaceship to be conserved when the spaceships have stopped it has to go somewhere. This energy will do work in deforming the spaceships? Correct?

50 KE per spaceship will be used for (bad) work.

**Two spaceships, A and B, with mass 1, velocity 20 and 0, collide head on.**

*Before collision:*

```
KE = 0.5 * mass * velocity^2
**Spaceship A**
KE = 0.5 * 1 * 20^2
KE = 200
**Spaceship B**
KE = 0.5 * 1 * 0^2
KE = 0
```

*After collision:*

Assuming they deform and “stick” together, for momentum to be conserved (which was previously (20*1) + (0*1) = 20) they must move together at 10m/s (10*2 = 20).

```
KE = 0.5 * mass * velocity^2
**Spaceship A+B**
KE = 0.5 * 2 * 10^2
KE = 100
```

For the 200 KE of energy to be preserved 100 KE (200 KE - 100 KE), 50 KE per spaceship, will be used for (bad) work in deforming the spaceships.

As such, this collision will be similiar to the previous collision.

**Two spaceships, A and B (yo mamma), with mass 1 and 99, velocity 10 and 0, collide head on.**

*Before collision:*

```
KE = 0.5 * mass * velocity^2
**Spaceship A**
KE = 0.5 * 1 * 10^2
KE = 50
**Spaceship B**
KE = 0.5 * 99 * 0^2
KE = 0
```

*After collision:*

Assuming they deform and “stick” together, for momentum to be conserved (which was previously (10*1) + (0*99) = 10) they must move together at 0.1m/s (0.1*100 = 10).

```
KE = 0.5 * mass * velocity^2
**Spaceship A+B**
KE = 0.5 * 100 * 0.1^2
KE = 0.5
```

For the 50 KE of energy to be preserved 49.5 KE (50 KE - 0.5 KE), 24.75 KE per spaceship, will be used for (bad) work in deforming the spaceships.

As such, this collision will be *not* similiar to the previous collision. This seems wrong to me, and having read around the subject I feel I must have made a mistake or have an incorrect assumption. Help!