# Gravity Help

1. Feb 19, 2010

Assume 2 bullets-- Exactly the same outside size and dimensions, Exactly the same velocity in OUR atmosphere.
One Bullet weighs more than the other--
You shoot them straight into the air-- which one hits the ground first?

How about if you shot them horizontally?

Is there any webiste that shows the proof or calculations for this problem?

2. Feb 19, 2010

### mathman

In general, two objects of the same shape and size, but different mass, will differ in terms of buoyancy, so the lighter one will fall more slowly.

3. Feb 19, 2010

Maybe I need to clearify my question and parameters.
Same exact size bullet
Same shape
Same Exact gun
One Heavy bullet One Lite
same velocity ( So the heavier bullet gets a higher charge to propel the bullet at the same muzzel velocity as the liter bullet.
Our Atmosphere ( Assume sea level any given temp)

Fired straight in the air-- both have to travel to they are out of energy for the climb then both have to reverse direction and free fall.

Which will land first-- the heavy or lite bullet

Is the answer the same if they are fired horizontally

4. Feb 19, 2010

### OME9A

I'm a beginner but maybe I can help put it in a simpler way--

Think of dropping a feather and a tennis ball at the same height. We learned that on the moon since there is no air resistance so they would reach the ground at the same time since the gravity and thus the acceleration is the same for both objects... But on Earth there's air resistance (or buoyancy? as the previous poster said) so the lighter object will be kept afloat longer. The feather would float around a bit and land after the tennis ball.

Therefore the lighter bullet will take longer to reach the surface...

5. Feb 20, 2010

### EWSwan

The basic argument of buoyancy is correct. Think about the basic force equation, F=ma. Initially both bullets are traveling at the same velocity. There are two kinds of basic forces acting on the bullet (to first-order): gravity and friction with the air, which I'll call "air resistance".

Gravity does not change, no matter what happens to the bullets' motions. The force on each is proportional to its mass, and if there were no air, they would follow identical paths, given that they start with identical velocities.

Air resistance is different. It has to do with the shape of the bullet and the viscosity (thickness) of the fluid (air). The bullets are identical in shape, so the backward-directed force due to air resistance is proportional only to each bullet's speed. And since they have different masses, they will decelerate differently. Initially traveling at the same velocity, they will experience the same force due to air resistance. Since F=ma, and the Forces are the same, and we know their masses are different, then their accelerations must be different. The lighter bullet will slow more quickly.

This is true for any horizontal motion. This is also true for vertical motion. The lighter bullet will not go as high. And assuming they both go high enough to fall long enough to reach terminal velocity (when the force of gravity pulling down is exactly balanced by the force of air resistance pushing up), the lighter bullet will fall more slowly.

Determining which bullet will land first requires solving the equations, including the equation for air resistance, which is something like F=kv, where v is the velocity and k is some constant factor that depends on the shape of the bullet and the properties of the air. And to be complete, you would need to include the fact that at high velocities, the air resistance is proportional to velocity-squared, not just velocity. (It might even be a higher power, something is telling me.)

Last edited: Feb 20, 2010