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# Why is it that a bullet fired from a gun comes down with the same velocity that it went up with?

Question #51106. Asked by eytank. (Sep 20 04 1:15 PM)

gmackematix

If there was no air resistance on the bullet then yes, the bullet would indeed hit the ground at the same speed as it was fired up.
Let the starting velocity be u m/s and its final velocity be v m/s. With only gravity acting downwards on the bullet, it would be constantly accelerating at 9.8 m/s/s from a negative velocity u m/s to 0 m/s at the top of its flight up to velocity v m/s at the end.
As the distances from the ground to the top and the top to the ground are the same and the acceleration is the same then the velocities are clearly the same only different in sign. In other words the speed it goes up is the same as the speed it went up.
Of course, in practice, air resistance means the speed it comes down will be a little less than the speed it went up.

Note that it is only the vertical component of the velocity we are talking about here. For example, if the bullet is fired up at 30 degrees then only about half the speed is directed upwards while 0.87 of it is directed horizontally. Those who know a bit of trigonometry should see why.

[Sep 20 04 8:48 PM] gmackematix writes:

I'm sure one of those ups should be a down. And I'm also up when I should be lying down so goodnight.

 Sep 20 04, 7:46 PM
peasypod

gmack is correct. If there was no air resistance, it comes down at the same speed as it was shot up. If there is air resistance, it returns with the terminal speed under the prevailing air conditions (determined by the shape and composition of the bullet).

 Sep 21 04, 4:10 AM

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