Is the speed of a bullet shot straight in the air the same as its speed when it falls down ?

Question

If I use a gun to shoot a bullent straight up (at 90 degrees) in the air, the bullent is going to leave the gun at a certain speed. So the question is: Is the speed of the bullet falling down the same as the speed of the bullet leaving the gun? (Is the answer the same if we don't consider the air friction?)

Answer 1

Yes.

The bullet decelerates as it continues up until it reachs it's highest point. It then begins to excelerate as it falls back down. A falling body continues to excelerate.

When it reaches the same elevation from which it was shot (it does not have to be shot straight up), it will be traveling at the same speed that it had when it let the gun, excluding any extra forces like wind or air friction, which you have ruled out.

In a airless environment like the moon, the speed would be exact, but of course earth does have air and wind which would keep the speeds from begin exactly the same.

Answer 2

In theory if you had no air friction, the gravity would add to the bullet's acceleration.

Though if you do some estimates (depending on nozzle speed and barrel length), you'll find that the acceleration due to the explosion of the charge is easily 100'000 times greater than that of gravity.

So the difference in speed between the bullet shot up, or down, would be very, very small.

Then however, the bullet would continued to be submitted to gravity, so depending on how long you waited, and again ignoring air resistance, and if you are hgih enough in the sky, the bullet shot up would eventually come to rest before starting to fall, whereas the bullet shot down would accelerate and accelerate and accelerate.

Now if you have air resistance, things won't be that different, except that the bullets will be slowed down by it, so the bullet shot up will go much less high (couple miles only) that it would have w/o air resistance. And the bullet shot downwards would not continue to accelerate, but rather would stabilise at some speed where the acceleration from gravity, and the deceleration (negative acceleration) from air resistance, match each other.

Hope this helps

Answer 3

A pistol shoots at about mach 1, a rifle can shoot a bullet at close to mach 3. As a bullet leaves the muzzle, it immediately begins to slow due to the air drag force.

Any falling object accelerates until air drag balances the force of gravity. The reason a feather falls slowly is that it's shape has a high drag coeffecient. The drag force balances it's weight at a slow speed.

A bullet will fall from high altitude and achieve this same drag balance, it will be just at a higher speed than a feather. Probably less than Mach 1... I would guess the balance would be found at 200 or 300 miles per hour.

Answer 4

The answer to this lies in an energy balance.

By firing the bullet you are putting energy into it. All this energy has to come out somehow. With air resistance, the bullet creates friction with the air, which disapates the energy as heat, thus the bullet be moving slower when it hits the ground than when you fired it.

Without air resistance, however, there is nowhere for the energy to go. As it goes up, the kinetic energy is converted to potential energy, the the potential energy is converted back to kinetic energy as it falls. With nowhere for the energy to go, the bullet has the same amount of energy for the whole flight, so (assuming the bullet has a constant mass) it must have the same speed at the begining and end.

Answer 5

If not for the frictional force of the air, the speeds would be the same as it wouldn't involve any work / loss-of-energy. But as the air factor kicks in the bullet needs to cut across the air to go up & in coming back, loosing some of its energy and hence speed.

Answer 6

1ST CASE NO FRICTION

it has to be the same sine energy is conserved. when shoot the bullet will have maximum kinetic enrgy that will be transformed to potential energy that will reach a maximum in maximum height where the velocity will be zero. then it eill start falling again till it reaches maximim speed and zero potential energy when crossing the height where it was shoot from.

now if there is friction, simply the air will consume energy due to the friction therefore when it return to the initial state the velocity will be smaller. simply with the same speed it would achieve bigger altitude therefore larger velocity if the friction was not present
now that there is friction its velocity will be smaller when it returns since frictions consumed same of its maximum original kinetic energy

Answer 7

You need to be more specific about which point in time you are considering the speeds. 1 second after the bullet is at its highest point and is starting to fall down it will not be as fast as it was when it left the gun.

Answer 8

If you ignore air resistance, the speed of bullet when it reaches the initial level is the same as the speed of firing. It can be proven from below.

Let u be initial speed of projection
Upward motion: v^2=u^2-2gs
0=u^2-2gh, h is maximum height
h=u^2/2g
Downward motion: v^2=u^2+2gs
=0+2gh=u^2
Therefore v=u if we only consider speed. Of course for velocity, v=-u

Answer 9

Speed going up is same as speed comeing down. If you ignore air friction
Trust me, we've done a million of these questions at school

Answer 10

The bullet is initially propelled at high speed when you first shoot it out of the gun.Loss of this propulsion force,together with gravity will cause it to slow down as it reaches the maximum height.It will then start to fall,unpropelled,but dragged downwards by gravity.But if you compare the propulsion force of the bullet as it travels upwards(about 300m/s),with gravity(9.8m/s),it obviously infers that the bullet travels upwards faster than when it is falling downwards,even when considering gravity.