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I need some help with a problem I want to solve.

You have a gunman standing 50 ft away from a human target. According to google, the average bullet travels at 2,500 fps. If my math is correct (debatable, my math skills are kind of sad) this gives the target .02 seconds or 20 ms to react before the bullet reaches them.

Also according to google, The average reaction time for humans is 0.25 seconds to a visual stimulus, 0.17 for an audio stimulus, and 0.15 seconds for a touch stimulus (Logically speaking, I believe this is the time between the initial stimulus and the time motion is initiated, not completed). I'm not sure (could not find) the amount of time would take this average human to actually finish moving their hand into a position to block the bullet's path if it is headed directly for the person's heart. Edit: couldn't find numbers online, so I found a victim and measured him. He is 6 ft tall, his arm is about 30 inches long from finger-tips to shoulder, and the straight-line distance between his hand and the approximate area of his heart was about 25 inches (2.08333 ft). So let's assume the hand needs to cover a distance of about 25 inches. I also found this statement: "The human hand can move 150 MPH(.04 miles per second which equals 215 feet per second" here: http://highdeas.com/lifestyle/This_is_insane_but_I_cant_disprove_it (but there was no reference to say where the number came from).

Edit 2: I checked the number with an online calculator and it would seem that 150 mph is actually 220 fps, not 215.

Obviously, average Joe (and even exceptional Bob) are far to slow to have a prayer of putting their hand in the way of a bullet (and even if they did, the bullet would rip a hole in their hand).

What I want to know is if it is possible to determine how many times faster than normal human reaction time Superman would need to be in order to block a bullet with his hand.

MarielS
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  • There are some data missing for me to give an answer. I would need to know the top speed of the hand and the expected distance between the hand and the heart. Throwing some numbers in, if he average human would take less than a second to finish his/her defence movement (think of martial arts specialists), then Superman would need to be around 50 times faster. – Ertxiem - reinstate Monica Apr 01 '19 at 01:01
  • Thanks, I'll look up a few more things an add as much as I can find – MarielS Apr 01 '19 at 01:02
  • @Ertxiem edited the original post – MarielS Apr 01 '19 at 01:17
  • Not much to do here. Your calculations of the bullet taking $0.02$ secons is correct and if you conversion of $150 mph$ to fps is correct then then $\frac {25}{215}=0.116$ seconds. Even with instantaneous reflex it can't be done, not if superman has normal hand velocity. But if his reflex is $k$ times faste and his speed is $m$ then you need $0.15/k + 0.116/m = 0.02$. If superman is $n$ times faster in all thing you need $0.15/n+0.116/n=0.266/n=0.02$ or superman is $13.3$ times faster in all ways. – fleablood Apr 01 '19 at 01:36
  • @fleablood: I did almost the same approach you did, but you also considered in separate the two different ways of being faster, nice! Regarding the computations, I saw a small mistake: you divided $25$ inches by $215$ feet per second. – Ertxiem - reinstate Monica Apr 01 '19 at 02:31
  • Update: I checked the number with an online calculator and it would seem that 150 mph is actually 220 fps, not 215. Also, https://physics.stackexchange.com/questions/33326/can-human-hand-move-at-a-speed-rate-like-this-baseball-pitch-or-is-it-just-the-s over on the physics stack indicates the top speed for a shorter motion might be about 100 mph, rather than 150. I ran some numbers and looked at how long it takes a pitcher to make a quick motion to release a ball, and decided it's a fair number to say a person may be able to move their hand from their side to their heart in about 0.03 sec. – MarielS Apr 01 '19 at 04:53
  • Alas, all this just means Superman probably needs to move even FASTER compared to our non-super human :( – MarielS Apr 01 '19 at 04:54

1 Answers1

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So, from your data, it seems that the average human would take around $0.25s$ from the moment he/she saw the gun firing to start the movement.

Then, the same human would need at least $0.01s$ to move the hand in front of the heart, assuming that the hand can immediately move at top speed.

Therefore, average humans would complete their defence movement in over $0.26s$ after they saw the gun firing.

Superman would need to be 13 times faster to do the same thing in $0.02s$, since $\frac{0.26}{0.02} = 13$.

By the way, looking at a related scientific article we can see that the reaction times of young male adults is around $0.226s$, so it's close to the estimates in here.

Ertxiem - reinstate Monica
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  • What if he started moving when he first heard, rather than saw, the gun fire? (oh boy, I just realized that the sound, and the light from the muzzle flash hitting the eye, both also take time to travel... but maybe for the sake of simplicity I should just ignore this) – MarielS Apr 01 '19 at 02:22
  • Then Superman would have to be $\frac{0.17+0.01}{0.02}=9$ times faster. It's still around $10$ times faster, so not much of a difference, considering that we are using approximate values. – Ertxiem - reinstate Monica Apr 01 '19 at 02:26
  • Neat. Thank you. I looked up the speed of sound (1125.328 fps) and it is actually slower than the bullet. So Superman is going to have to use his eyes! Fortunately for him, if my calculations are correct, light crosses a 50 ft distance in about 5.09 one hundred millionths of a second, which isn't going to slow him down much! – MarielS Apr 01 '19 at 04:21
  • So, revising your equation for what I discovered is a slightly more realistic (maybe?) time of 0.03 seconds for the hand movement, I believe that results in Superman needing to be 14 times faster. – MarielS Apr 01 '19 at 05:00
  • Yes, it would result in 14 times faster. By the way, if you think it's appropriate, you can accept my answer (there is a green button). – Ertxiem - reinstate Monica Apr 01 '19 at 12:30