Potato Bullet

I was watching a program on TV called 'What Happens if" which is a sort of 'try some idea out and see what happens, with some science etc ' thrown in. The episode I watched was all about 'what would happen if we shot a bullet out of a car  where the bullet is traveling at 60mph and the car is traveling at 60mph? Would the bullet just hang alongside the car?' Well I learned in primary school that this would not be the case.

If the Bullet was traveling at 60mph and the car was traveling at 60 mph then the relative speed of the bullet would be 120mph. (less given drag and deceleration). This was a no brainier and I felt that there was more that could be explored given this scenario. We know that :

1. The speed of the bullet relative to the car would be 60mph
2. The speed of the bullet relative to the ground (or an observer standing on the ground) would be 120mph
3. The speed of the car relative to the ground observer car would be 60mph

If they wanted to see the bullet 'hanging in the air next to them', (which is what they were trying to do) then they would need to fire the bullet from the ground and the exact moment the car passed the gun with the car going at the same speed as the bullet. They unfortunately did not try this as I would like to have seen it.

So we know that:

1. The bullet, relative to the ground observer would be traveling at 60mph
2. The car, relative to to the ground observer would be traveling at 60mph
3. The bullet, relative to the car would be traveling at 0mph, as are both the same speed.
4. The ground, relative to the car and the bullet would be traveling at -60mph. 

so this is case (excusing the drag, deceleration etc that would make this a lot more complicated) the passenger in the car would see a bullet 'floating' next to him just outside the car, while the ground observer would see the car and the bullet 'shoot' past at 60mph.

 An interesting question comes in when the passenger reaches out and grabs the bullet. Although the bullet is traveling, relative to him, at 0mph, the bullet still has momentum. What would happen to that momentum when the passenger grabs the bullet?  I assume that the momentum would either be passed to the passenger.. or not..

 If you know the answer to this please reply..

 The irony of this blog is that right now I'm a passenger in a taxi traveling at rather more than 60mph...... where's the bullet?