The Fate of a Bullet Shot Straight Up: Gravity's Pull and Terminal Velocity

Have you ever wondered about the journey a bullet takes when shot straight up into the air? Given the Earth's gravity and air resistance, the bullet's path is a fascinating study of physics. Let's explore the steps a bullet takes from the moment it leaves the gun barrel until it eventually comes back to earth.

Initial Velocity and Gravity's Effect

When a bullet is fired straight up, it starts with an initial upward velocity equal to the handgun's muzzle velocity. On Earth, gravity acts continuously to reduce this velocity. Gravity pulls the bullet down at a rate of 32 feet per second squared (ft/s2) for every passing second. If a bullet is fired at a muzzle velocity of 3200 ft/s, it will lose all its upward velocity within approximately 100 seconds due to the constant pull of gravity. This principle is well illustrated by the famous example of the wreckage from an Unmanned Aerial Vehicle (UAV) that plummeted into a backyard from thousands of feet in the air.

The Role of Air Resistance

Aside from gravity, air resistance plays a critical role in slowing the bullet down. The bullet's velocity is further reduced by air friction, which works continuously to slow it down as it ascends. This dual force of gravity and air resistance works in tandem to bring the bullet to a halt as it reaches its peak altitude.

Reaching Zero Velocity and Falling Back Down

As the bullet's upward velocity reaches zero, it stops momentarily. Then, due to the continuous pull of gravity, the bullet begins to fall back towards Earth, picking up speed as it descends due to the 32 ft/s2 gravitational acceleration. The bullet will reach its terminal velocity, which is the maximum speed it can attain in the air, limiting its fall due to increasing air resistance.

Terminal Velocity and Impact

Terminal velocity is the point at which the drag forces and gravitational forces are balanced, meaning the bullet no longer accelerates. In the case of a bullet, this can occur at a speed of several hundred feet per second or more, depending on the bullet's shape and air resistance. Upon impact, the bullet can cause significant damage due to its high speed. The impact can be further complicated by the Earth's rotation, which can affect the landing point of the bullet, causing it to land at a different location from where it was fired.

Earth's Rotation and Bullet Trajectory

It's important to note that the Earth's rotation plays a role in the bullet's trajectory. Although the bullet is shot straight up, local effects such as the air's resistance and the Earth's rotation lead the bullet to land with a slight drift from its initial launch point. This drift is minimal and often negligible, but it can become more significant over long distances and higher altitudes.

Conclusion

The journey of a bullet shot straight up is a reminder of the fundamental principles of physics. Gravity and air resistance are the two main forces acting on the bullet, dictating its upward and downward motion. Understanding these forces is crucial for anyone interested in ballistics and aerodynamics. As the old saying goes, "Whatever goes up must come down," and this holds true for any projectile launched against the Earth's gravity.