A gun is fired parallel to the ground. At the same instant, a bullet of equal size and mass next to the

muzzle is released and drops to the ground. Which hits the ground first and why?

I think that the bullets will hit the ground at the same time because the bullet that is fired is shot at a faster speed and travels a longer distance, while the dropped bullet has a slower speed and travels less distance. The two factors cancel out?

In the absence of other factors, both will hit the ground at the same time, because the force of gravity is all that's acting on them, making them fall at the same speed.

The horizontal speed of the bullet has no effect on the pull of gravity.

However, in real life, the aerodynamics of the fired bullet will probably keep it aloft a bit longer than the falling bullet.

Actually, the bullet that is fired will hit the ground first. This is because both bullets experience the same acceleration due to gravity, regardless of their speeds or distances traveled. The horizontal motion of the fired bullet does not affect its vertical motion, as they are independent of each other. Therefore, the fired bullet will hit the ground before the dropped bullet.

Yes, you are correct. Both bullets will hit the ground at the same time, regardless of their initial velocity.

To understand why they will hit the ground simultaneously, let's consider the basic principles of motion and gravity.

When the gun is fired, the bullet moves horizontally parallel to the ground with an initial velocity, while the bullet released next to the muzzle drops vertically downward due to the force of gravity.

Let's break down the motion of each bullet separately:

1. Bullet fired from the gun:
- The bullet is initially given a forward velocity by the gun.
- While moving horizontally, the bullet is also pulled downward due to the force of gravity acting upon it.
- This downward pull doesn't affect the horizontal motion of the bullet; it only affects the vertical motion.
- As a result, the bullet falls towards the ground due to gravity, but it maintains its forward velocity.
- Since the bullet is moving both horizontally and vertically, its path is a curved trajectory called a projectile motion.

2. Bullet dropped from the muzzle:
- The bullet is released with zero forward velocity, so it only experiences downward acceleration due to gravity.
- As it falls, its speed increases continuously because it accelerates due to gravity.
- The bullet follows a vertical straight line trajectory towards the ground.

Now, comparing the two motions, we can see that even though the bullet fired from the gun travels a greater distance horizontally, it also experiences downward acceleration due to gravity. At the same time, the bullet dropped from the muzzle accelerates vertically solely due to gravity.

The key point is that both bullets experience the same acceleration due to gravity since they are at the same location on the Earth's surface. This means that the vertical acceleration acting on both bullets is the same.

Therefore, regardless of their initial velocities and horizontal distances traveled, both bullets fall towards the ground with the same acceleration and will hit the ground simultaneously.

Hence, the bullets will hit the ground at the same time, as you correctly concluded.