- #1

Sairen

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I'm sure this topic has come up before, however, it was always under the requirements of being realistic, i.e. taking drag, air resistance, Earth rotation and what not into account. Also, I couldn't find any equations so that I can do the math myself. Hence, here is my question:

Suppose I shoot a bullet at 400m/s vertically into the air, I keep reading that it would arrive on the ground at the same speed. Now, I am a really not good at math, but I "know" that under the gravitational force of the earth, any object falls (counting air density, resistance, rotation, etc. out) at the speed of 9,81m/s.

I find it hard to imagine that, knowing this, a bullet would accelerate to its initial speed. So, I wanted to calculate it myself. Here comes the math:

I figured, if the bullet has a speed of 400m/s, then gravity would stop the bullet after aprx. 8154,94m (h = u² / 2g). Knowing its speed, that would mean it would take the bullet 20,39 seconds.

If the bullet arrives at the ground with the same speed, shouldn't it also arrive within the same time frame? I calculated that it will actually take the bullet 40,77 seconds to reach ground (t = √(2d/g)).

That means that the speed of the bullet is actually 199,98 m/s (v = ½ ⁎ g ⁎ d), so half as fast.

m=meters

s=seconds

h=height

u=initial velocity

g=gravitation

d=distance

v=velocity

Now, I am sure I made a super obvious mistake here, probably using the wrong equation or a simple, logical mistake.

Would anybody please be so kind and point it out to me and, if possible, provide with a correct trail of though/math so that I don't have to send the university of illinois physics department an email? :)

Thanx so much!