Understanding the Physics
* Gravity is the Key: The only force acting on both bullets in the vertical direction is gravity. Air resistance mainly affects their horizontal motion.
* Independent Motion: The horizontal motion of the fired bullet and the vertical motion of the dropped bullet are independent of each other. This is a fundamental concept in projectile motion.
Why They Hit at the Same Time
1. Vertical Motion: Both bullets start with zero vertical velocity. They both accelerate downwards due to gravity at the same rate (approximately 9.8 m/s²). This means they cover the same vertical distance in the same amount of time.
2. Horizontal Motion: The fired bullet has an initial horizontal velocity, but this doesn't affect its vertical motion. Air resistance will slow it down horizontally, but it won't change the time it takes to fall.
The Impact of Air Resistance
* Fired Bullet: Air resistance will slow down the fired bullet horizontally, causing it to land slightly closer to the gun than it would have in a vacuum.
* Dropped Bullet: Air resistance might slightly delay the dropped bullet's descent, depending on its shape and weight.
Conclusion
Even with air resistance, the fired bullet and the dropped bullet will hit the ground at roughly the same time. The horizontal motion of the fired bullet is mostly independent of its vertical descent. The impact of air resistance will be primarily on the horizontal distance traveled, not the time it takes to fall.
