I got into a discussion at work and need this question answered. One of us thinks if you are traveling 500 Fps and shoot a gun out the window and the bullet normally travels 1000 Fps it will now be traveling 1500 Fps. THe other one of us thinks the bullet will still be traveling at 1000 Fps. Please help end this.

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The bullet will be moving at 1500fps relative to an observer at rest relative to the shooter moving at 500fps. The shooter considers himself to be at rest so the bullet is traveling at 1000fps relative to him, while an observer at rest relative to the shooter must add the shooters speed to the bullets 1000fps, making the bullets speed 1500fps relative to him.

Now, it doesn't sound like your interested in the different frames so the big picture is that the bullets speed relative to the ground beneath your feet is 1500fps.

At those speeds the answer would be 1500 fps. If the speeds were close to the speed of light then it would be more complicated. But for the sake of your argument, it's safe to say 1500 is the right answer.

double post...

An observer from the vehicle would measure the projectile at the normal 1000fps. An observer on the ground would measure it as 1500fps (the velocities of the vehicle and projectile would in fact be additive from his point of view).

This is of course not taking into account the added air resistance the extra 500fps would add, etc etc etc.

Just for the sake of coolness, if the vehicle were going forwards at 1000 ft/s, and the gun were fired backward (the opposite of the direction the vehicle were headed) with equal velocity 1000 ft/s, the bullet would appear to simply drop as if dropped from someone's hand to an observer on the ground :D