Projectile motion - bullet shot from a rifle

[pst535]

Homework Statement

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?

Homework Equations

None

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.
This answer, obviously, is wrong.
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?

 

[Nathanael]

If we're ignoring air drag, then the bullet will keep moving - at a constant velocity (forever).

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.

 

[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?

 

[Nathanael]

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?

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.

 

[HalfLostAndSearching]

The reason both bullets will hit the ground at the same time is because they experience the same acceleration due to gravity, regardless of their initial horizontal velocity. This is known as the principle of independent horizontal and vertical motion.

When the rifle is fired, the bullet is given an initial horizontal velocity, but it also experiences a downward force due to gravity. This results in the bullet's trajectory being a curved path, known as a parabola. However, the vertical component of the bullet's velocity is always changing due to the constant acceleration of gravity, while the horizontal component remains constant.

On the other hand, the bullet that is dropped from rest also experiences the same downward force due to gravity, resulting in the same acceleration. This means that both bullets will fall the same vertical distance in the same amount of time and hit the ground at the same time.

In conclusion, the horizontal velocity of the bullet fired from the rifle does not affect its vertical motion, and both bullets will hit the ground at the same time. This is because the acceleration due to gravity is the same for both objects, regardless of their initial horizontal velocities.