Bullet fired from a moving train.

[Pinkk]

Homework Statement

A person is standing on a train that is moving 200 km/h to the right. The person fires a bullet that travels 200 km/h opposite the direction of the train's movement. How fast is the bullet moving according to the shooter's perspective (assuming there is no gravity, resistive forces, etc).

Homework Equations

Velocity of the bullet relative to the Earth = Velocity of the bullet relative to the train + velocity of the train relative to the earth

The Attempt at a Solution

Since the Velocity of the bullet relative to the Earth is -200 km/h and the velocity of the train relative to the Earth is 200 km/h, the Velocity of the bullet relative to the train is -200 km/h - 200 km/h = -400 km/h. Is this answer correct?

 

[Doc Al]

Correct. The speed of the bullet with respect to the shooter/train is 400 km/h.

 

[Pinkk]

That's what I thought, but I keep getting conflicting answers from different people because the question is somewhat ambiguous. I guess this is not a totally related physics question, but if a gun fires a bullet with muzzle velocity X, that's the speed of the bullet relative to the earth, correct? People say it'll be the velocity of the bullet relative to the train, making the velocity of the bullet relative to the Earth 0, so if you fire a bullet from the back of train at the same speed of the train, the bullet would just drop straight down to the ground.

 

[DaveC426913]

Yes, there is some ambiguity.

The question says the bullet has a velocity of 200km/h but it does not specify if that is relative to the gun or the ground.

My assumption would be the former. Thus, my answer is -200km/h relative to the shooter.

 

[Doc Al]

That's what I thought, but I keep getting conflicting answers from different people because the question is somewhat ambiguous.

The question is oddly worded. Did you present it exactly it was given to you? When I first saw "The person fires a bullet that travels 200 km/h" I immediately assumed they meant muzzle velocity, but since they ask for the muzzle velocity I thought that it must be the speed of the bullet with respect to the ground. To avoid ambiguity, when they mention a speed they must specify with respect to what. (Sloppy question!)

I guess this is not a totally related physics question, but if a gun fires a bullet with muzzle velocity X, that's the speed of the bullet relative to the earth, correct?

No, the muzzle velocity is the speed of the bullet with respect to the gun.

People say it'll be the velocity of the bullet relative to the train, making the velocity of the bullet relative to the Earth 0, so if you fire a bullet from the back of train at the same speed of the train, the bullet would just drop straight down to the ground.

That's correct. If the muzzle speed was -200 km/h and the train speed was +200 km/h, then the speed of the bullet with respect to the ground would be zero.

 

[Pinkk]

It wasn't technically a homework question, it was a question posed on another forum. So I'm guessing they meant the muzzle velocity, in which case I guess I'm wrong. Thanks though!

 

[Doc Al]

The person fires a bullet that travels 200 km/h opposite the direction of the train's movement.

If that means muzzle velocity, then the question seems rather silly:

How fast is the bullet moving according to the shooter's perspective (assuming there is no gravity, resistive forces, etc).

It's like saying: If the speed of the bullet is X with respect to you, how fast is the bullet moving with respect to you.

But I agree: Ambiguous wording!

 

[DaveC426913]

If that means muzzle velocity, then the question seems rather silly:

It's like saying: If the speed of the bullet is X with respect to you, how fast is the bullet moving with respect to you.

But I agree: Ambiguous wording!

This has been my thinking as well.

 

[pr0blumz]

Correct. The speed of the bullet with respect to the shooter/train is 400 km/h.

I agree.