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During a conference I have listened that an employee of an armed force, said that a projectile fired upwards the impact with my body it hurts less than when it drops downwards.

In my opinion all this is false if we do not assume in the meantime that there is air resistance (friction) and from what height it is fired. Obviously if the air resistance is zero the initial velocity of the projectile $v_0$ will be equal to the final velocity of the same when it reaches the ground.

Is there a mathematical/physical demonstration to refute this thesis?

ADDENDUM 1: I simply don't agree because if I was facing a balcony and someone shoots me from the ground at an altitude $h>h_0=0$ it hurts less if the same bullet falls on my head at the time of the descent?

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  • $\begingroup$ What's not clear? Why is there a closure? I have explained what has been asked of me and what I have heard. $\endgroup$ – Sebastiano Mar 25 at 22:36
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Can you please add some context on what are you trying to compare exactly? I might be oversimplifying the problem, but the way I see it, I would agree with the employee:

  • If the maximum height of the projectile fired upwards is equal to the height the other projectile is dropped, then we would have around the double of time to run away (thus less dangerous in that sense);

  • If the time to run away is equal in both cases, it means that the maximum height is smaller in the former case, thus the impact velocity if lower, being again the first case, less dangerous.

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  • $\begingroup$ No :-) I must not escape in any way. $\endgroup$ – Sebastiano Mar 25 at 22:35

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