# Projectile motion - bullet shot from a rifle

1. Aug 14, 2014

### pst535

1. The problem statement, all variables and given/known data
At the instant a horizontally held rifle is fired over a level range, a bullet held at the side of the rifle is released and drops to the ground. Which bullet, the one fired downrange or the one dropped from rest, strikes the ground first?

2. Relevant equations
None

3. The attempt at a solution
My answer: The one dropped from rest strikes the ground first. If we're ignoring air drag, then the bullet will keep moving - at a constant velocity (forever); the bullet that is dropped will accelerate toward the ground, acting under the influence of gravity; thus the dropped bullet will hit the ground first.
Right answer: both bullets fall the same vertical distance with the same acceleration g due to gravity and therefore strike the ground at the same time.
But I don't understand why this is the case, even after reading that. Can someone help me out?

2. Aug 14, 2014

### Nathanael

Aren't moving objects also attracted to the Earth? If the Earth is applying a force on the bullet, then why would it move at a constant velocity forever?

Are you implying that air drag is what causes bullets to fall?
Or are you implying that bullets don't fall? (until they hit something)

edit:
This problem demonstrates the independence of vertical and horiztonal motion (or any perpendicular directions, for that matter)

I've asked a few people this question, and the consensus is that it's counter-intuitive. If I remember correctly, I too got it wrong when I first heard it.

Last edited: Aug 14, 2014
3. Aug 14, 2014

### pst535

I don't really know what I was implying. I think I just don't get it. And also, doesn't the bullet shot out of the rifle have a higher initial velocity, or something? Wouldn't that increase the time it takes for the bullet out of the rifle to hit the ground?

4. Aug 14, 2014

### Nathanael

It has a higher initial velocity, but the initial velocity is 100% in the horizontal direction.
(So it has no effect on the vertical displacement)

If the gun were pointed even slightly upwards, it would take longer to hit the ground.

If the gun were pointed even slightly downwards, it would hit the ground first.