What Happens When You Fire & Drop a Bullet from a 2 Story Building?

[eric.rumery]

If you are standing atop a 2 story building and fire a bullet vertically towards the ground and drop one from the same height will they arrive at the same time? I am not a physics person but my girlfriend is in it now and tells me that they would arrive at the same time. I don't see this to be true due to the second force acting upon the fired bullet. Can someone please explain this to me in lamens terms. I believe the fired bullet rotate on an axis increasing its terminal velocity anyway?
Thank You,
Eric

 

[rcgldr]

If you are standing atop a 2 story building and fire a bullet vertically towards the ground and drop one from the same height will they arrive at the same time? I am not a physics person but my girlfriend is in it now and tells me that they would arrive at the same time. I don't see this to be true due to the second force acting upon the fired bullet. Can someone please explain this to me in lamens terms. I believe the fired bullet rotate on an axis increasing its terminal velocity anyway?

You need to clean up the wording here, the bulled is fired horizontally, and the other bullet dropped at the same time the first bullet leaves the barrel. With no atmoshpere, and a relatively flat earth, both bullets land at the same time.

With an atmosphere, the fired bullet will take a bit longer to fall than it would without an atmosphere, but so would the bullet dropped. I suspect if the bullet dropped started tumbling (rotating at a high rate), it would hit the ground later.

Ignoring the overly techinical stuff, the point here is that horizontal motion doesn't affect the vertical motion.

 

[sir-pinski]

Hi Eric,

Thank you for bringing up this interesting question. The answer to whether a fired bullet and a dropped bullet from the same height will arrive at the ground at the same time is actually a bit more complex than it may seem.

In theory, if we ignore air resistance, both bullets would indeed reach the ground at the same time. This is because the only force acting on both bullets is gravity, which causes objects of different masses to accelerate at the same rate. This is known as the principle of equivalence.

However, in reality, air resistance plays a significant role in the motion of objects. When a bullet is fired, it experiences two forces - the force of gravity pulling it towards the ground and the force of air resistance pushing against it. This air resistance slows down the fired bullet, making it take longer to reach the ground compared to the dropped bullet which experiences only the force of gravity.

Additionally, as you mentioned, the fired bullet also experiences a second force - the force of the gunpowder explosion propelling it forward. This force causes the bullet to initially accelerate faster than the dropped bullet, but as the air resistance increases, it eventually reaches its maximum velocity and then starts to slow down. This means that the fired bullet will take a longer path to reach the ground compared to the dropped bullet, and therefore, they will not arrive at the same time.

In terms of the rotation of the fired bullet, it is true that it will rotate on its axis as it travels through the air. This rotation can affect its trajectory and make it more prone to air resistance, which can further slow it down. However, this rotation does not significantly impact the overall time it takes for the bullet to reach the ground.

I hope this explanation helps to clarify the concept for you. Keep asking questions and learning more about physics - it's a fascinating subject!