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?