# Train moving at velocity v relative to earth

1. Aug 16, 2009

### mr.physics

train moving at velocity "v" relative to earth

My question is a basic one so patience would be appreciated =)

Say we have a train moving at velocity "v" relative to the Earth. A man standing inside shoots a bullet at velocity "w" relative to the train's motion. The bullet should thus move at a speed of "v+w" relative to the Earth.
I find this almost counter-intuitive. The speed the bullet attains is dependent only on the force exerted on it by the gun, regardless of how fast the gun is moving. It seems to me the bullet should retain its original speed "w". Although I am obviously wrong it would be helpful if someone could explain to me why.

Thanks!

Last edited: Aug 16, 2009
2. Aug 16, 2009

### pgardn

Re: Motion

What would the velocity of the bullet be relative to the earth if the man was just holding the bullet?

3. Aug 16, 2009

### drizzle

Re: Motion

hey mr.physics, welcome to PF,

maybe you would get it if you imagine the train’s speed as c [which is the speed of light] relative to the earth, would the bullet’s speed remains w relative to earth or w+c? [actually you may say that the bullet’s speed ~c, you may ignore w compared to c]

hope I’m not complicating things here

4. Aug 16, 2009

### lstellyl

Re: Motion

So as pgardin pointed out here is what I think is important to understanding this concept...

if you are in a moving train and drop the bullet, someone on the ground would see the bullet move forward with a velocity ~v.

this would be correspondent to 0 force applied from the gun, yet it still has a positive velocity relative to the earth based on the velocity of the train and objects on it "pulling" it along at that speed.

now add the explosive force of shooting the gun... this will add the extra velocity w to the bullet, where someone on the train would observe the bullet going at velocity w, and people off the train observing it going at v+w.

5. Aug 16, 2009

### mr.physics

Re: Motion

In shooting the gun however, nothing makes contact with the bullet besides the gun (which is moving at v).

6. Aug 16, 2009

### Phrak

Re: Motion

Ummm. No. This is the part you have wrong. As other have said, the velocity is due to both.

Last edited by a moderator: Aug 16, 2009
7. Aug 16, 2009

### Staff: Mentor

Re: Motion

The point of that question was to get you to realize that even without your hand exerting a force on it, the bullet is still moving wrt the earth. Because...
The speed of the bullet wrt your hand is zero. The speed of the bullet wrt the earth is 0+v. Now apply that to the gun...

8. Aug 17, 2009

### Danger

Re: Motion

Just a matter of terminology:
Mr. Physics didn't specify the vector of 'w' relative to the train. If the gun were fired toward the rear of the train, would the proper expression be v + (-w), or just v - w? What about it being fired at some arbitrary angle such as 45°?

Last edited: Aug 17, 2009
9. Aug 17, 2009

### pgardn

Re: Motion

I would ask myself not to worry about what did or did not put the bullet into motion relative to the train. I would just ask myself what is the speed of the bullet when it is motionless with respect to the train. I then I would ask myself what it the speed of the bullet with respect to the earth in the same situation. Then continue the logic from there... No need in resorting to information that is not pertinent to the question... Forces, ect... we are just concerned with speed or velocity relative to certain objects.

10. Aug 17, 2009

### Staff: Mentor

Re: Motion

Hi mr.physics. Remember that force is mass times acceleration. This means that when you fire the gun its force (or impulse) causes a specific change in velocity. Since the initial velocity is higher the same change in velocity leads to a greater overall velocity.

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