Proof of 2v Velocity When Gun Fired Aboard Plane

[eddie]

If a gun fires a bullet at a velocity v and is then taken aboard a plane traveling at a velocity v and is fired again in the direction of travel ,what is the simplest proof that the bullet's new velocity is now 2v ?

 

[A.T.]

See:
http://en.wikipedia.org/wiki/Galilean_transformation

But note that it only apples when v << c.

 

[eddie]

See:
http://en.wikipedia.org/wiki/Galilean_transformation

But note that it only apples when v << c.

Thanks for your reply I was looking for a simple proof using Newton's Laws of motion.

 

[Dale]

Newton's laws are invariant under a Galilean transformation.

 

[pmacias]

The simplest proof that the bullet's new velocity is now 2v when fired aboard a plane traveling at a velocity v is through the principle of relativity. According to this principle, the laws of physics remain the same in all inertial reference frames. In this scenario, the first firing of the gun and the second firing of the gun on the plane can be considered as two separate inertial reference frames.

In the first scenario, the gun is fired from a stationary position on the ground with a velocity v. In this reference frame, the bullet will travel with a velocity v.

However, in the second scenario, the gun is fired from a moving plane with a velocity v. In this reference frame, the bullet will travel with a velocity v + v (due to the velocity of the plane). According to the principle of relativity, the laws of physics should be the same in both reference frames. Therefore, the velocity of the bullet in the second scenario should also be v.

However, we observe that the bullet's velocity in the second scenario is v + v, which is equal to 2v. This indicates that the bullet's velocity has doubled when fired aboard the plane. This can be mathematically represented as 2v = v + v.

In conclusion, the simplest proof that the bullet's new velocity is now 2v when fired aboard a plane traveling at a velocity v is through the principle of relativity, which states that the laws of physics remain the same in all inertial reference frames.