# Homework Help: Force of impact on a human body falling into water

1. Aug 12, 2008

### aleiss

1. The problem statement, all variables and given/known data
A 50lg man jumps off a bridge 80m high. He lands in choppy salt water feet first. Each foot has an area of 75cm^2. The goal is to find out

a) What is the force sustained by the human body while hitting then decelerating in the water.
b) depth of penitration

Because this is to check the safety of the jump, ie safe, harmful, or deadly, we can simplify it by ignoring the temperature of the water and air.

known figures.
Salt water = 1.027 g/cm^3
bridge = 80m
total penetration area = 150cm^2
weight of man = 50kg

2. Relevant equations

from the bridge to the water in time
9.8m*s^2 = h

force in a fluid
f= 1/2p*v^2*c*a
because I did not know what the drag coefficient of a human is (a flailing human) I ignored it, and it is unitless.

3. The attempt at a solution
I did not know how to calculate the velocity so I calculated the speed
9.8m*s^2=h
9.8m*s^2=80m
s^2=8.15
s=2.85

I read that at 3 seconds an object has 29.2m/s so I guessed (not very scientific I know) and said 2.85 would be 28m/s

f= 1/2p*v^2*c*a
we nix the c
f=1/2*1.027g/cm^3*2800cm/s^2*150cm^2
f=6*10^8 g*cm^4*s^2/cm^3
f=6*10^8g*cm*s^2
thats ergs right?

Anyway, this is a rough figure but ok for my purposes. I do not know what do to with this figure not though as I want to calculate the amount of force sustained on the body when it hits and as it decelerates as well as how far down it can go.

I have this other equation
Vf^2 = Vo^2 + 2*a*y
but I do not really know what to do with it.
this is not for any scholastic or commercial project (I am a high school drop-out). Rather there is a bridge near me (the sunshine skyway) which is famous for people jumping off it to commit suicide. I am arguing that they survive the fall and then drown.

Thanks for any help given.

2. Aug 12, 2008

### Dick

The potential suicide will land at velocity of about 40m/s, ignoring air friction. That's about 90mi/hr. Air friction will reduce that somewhat, but you are probably in the right ballpark for velocity. Beyond that the question gets much harder. Force isn't measured in ergs. That's energy. What will kill you is the acceleration. How long does it take the water to brake you to a halt and what does that translate into g's of acceleration, and for how long is that applied. That's fluid dynamics. And then you have to figure out the mortality rate given those parameters. I don't know how to do either. I would guess a belly flop would do serious damage. Entering feet first would probably be survivable. But that's a guess. I think your best bet is to look for accounts of falls from such a distance and what was the outcome. Physical calculation may not be the best way of answering this. But kudos to you for trying.