can you help me with a basic physics problem?

Question

A bullet is fired horizontally from a pistol, and another is dropped simultaneously from the same height. If air resistance is neglected, which bullet hits the ground first? Please explain for me.

Answer 1

The bullet's vertical motion is governed by the vertical forces only and not governed by horizontal and vice versa.
In each case the bullet's vertical motion is governed by gravity acting on itself. The gravity force gives an acceleration of 9.81 met/sec squared. Both have the same distance to go through and both have a initial vertical velocity of 0. Therefore they both reach at the same time, neglecting air friction.

Answer 2

Yes they both hit the ground at the same time

The reason they do is that any velocity or acceleration vector (has magnitude and direction) and can be represented as the sum of two component vectors which are mutually perpendicluar and independent. The vertical component for the two bullets is equal and due to gravity and so if they start at the same height they will hit the ground at the same time. Note: if the bullet was not fired horizontally then they would not land at the same time. Also, the curvature of the earth would make the horizontally fired bullet land a very small amount of time later.

Answer 3

They will hit the ground at the same time. Forget the fact that one is moving forward. That doesn't enter the equation at all. The only important thing is that the ONLY force pulling the two objects downward is that of gravity and it pulls equally on both objects. The reason you're having trouble understanding this is that few people other than physicists understand motion. Most people think that when you apply force to a ball that it's something like putting gas in a car. If you have this erroneous view, you think the ball eventually stops because it runs out of "gas", the energy you put in it. If you think this way you naturally assume the dropped bullet will hit the ground first because the gun applied more energy to it's bullet. Wrong. The only reason you apply force to either the baseball or the bullet is to cause it to accelerate - pick up speed, from zero mph in this case. The force applied by gravity on the two bullets is completely independent of the forward acceleration that the gun gave its bullet or the forward acceleration that you didn't give the one you dropped.

Answer 4

That's odd.. I have no physics background whatsoever, but despite the initial impulse to suggest that gravity would change the flight direction of the bullet and therfore redirect it's path downwards like a crashing plane; it doesn't, because there's no thrust beyond the act of being fired.. there's no continual thrust to drive it into the ground. There's inertial horizontal travel, but that's all.

If there is no wind resistance factor, the fired bullet can't "glide" at all either, so it falls to the ground just as quickly as the one that was dropped, just a lot further away.

The horizontal movement has no impact on the amount of gravitational pull. There could be an argument suggesting that the spin of the fired bullet acts as a gyro, making it more resistant to gravitational forces, but I think you'd be hard-pressed to prove it.

As a result, they both hit the ground simultaneously.

Answer 5

Both hit the ground at the same time.

The horizontal velocity doesn't change anything. Both have the same initial height, same vertical velocity (zero), and same vertical acceleration (-9.8 m/s^2).

The governing equation is.

y = 0.5*a*t^2 + vo*t + yo

where vo is zero, y is zero, yo is the initial height and a is -9.8

note: since air resistance is neglected, the shape of the bullet is no longer a factor and this is a key component as to why the acceleration is the same.