# Falling off of a building and ANY equations that would be associated with that

1. Jan 3, 2010

### Meprathe

Basically I got in trouble at college for going onto my dorm roof to get my frisbee so what I have to do is write a 3 page paper about what would happen to someone if they fell off of a 4 story building (17 meters tall). Obviously they would die more times than not. But I need to discuss what laws of physics would come into play (asides from gravity). I was hoping someone could tell me what specific equations someone could use to calculate the amount of force in pounds would be present at impact with the ground, I weigh 160 pounds. Are there any other equations someone could use to calculate how long it take for someone to hit the ground from 17 meters up high as well. And any other equations you can think of that would play a part in this situation. Please help me I cant register for classes until this essay is finished! Thanks alot!

2. Jan 3, 2010

### whome9

50% mortality is something over 36 feet, but the people who live and fall from that distance need physical therapy for the rest of their lives.

As to the force when you land, it depends on how fast you decelerate. If you land flat and your body is only compressed a few inches there will be very high forces on you.
And bones have the strength of cast iron, but probably not its brittleness.

I know of one guy who fell 10 stories and landed on his feet. His tibias went through the soles of his feet and they had a picture of said feet.

Another way is to calculate 1/2 MV^2. This energy has to be dissipated, and the less time it takes to dissipate it, the more [destructive] power.

10g's or more may kill most people. Check out Colonel John Stapp's rocket sled stuff.

3. Jan 3, 2010

### rock.freak667

Well you could assume you walk off the building with some velocity v and use parabolic motion equations to calculate the time it takes to fall 17 meters. Though these equations along with most others are ignoring frictional effects.

4. Jan 4, 2010

### danielatha4

$$\Delta$$X=Vot+1/2at2

where a is the acceleration due to gravity, which is 9.8 m/s2

17 meters = 0 * t + 4.9 t2
17/4.9 = t2
t = $$\sqrt{17/4.9}$$ which approximately equals 1.863 seconds to hit the ground

Final velocity (upon impact) can be calculated by

Vf=Vo+at
Vf= 0 + 9.8 * 1.863 which equals approximately 18.257 m/s which is equivalent to hitting the ground at 40.8 mph... ow...

Of course this also demonstrates the conservation of energy

$$\Delta$$PE = $$\Delta$$KE

mgh=1/2mv2

160 pounds = 160*4.4 Newtons (conversion) = 704N
704N = m * 9.8 (gravity)
704/9.8 = m = 71.837 kg

back to mgh=1/2mv2
71.837*9.8*17=.5*71.837*v2
9.8*17 / .5 = v2
v = $$\sqrt{9.8*17 / .5}$$ = 18.254 m/s

Pretty much the same velocity

Figuring out impact:

Assume an amount of time it takes to impact the ground, or for your velocity to reach zero after intial contact with the ground. I'm not good at estimating that stuff. Maybe .5 seconds? or lower. Divide your final velocity by impact time and that will your deceleration. Multiply that by your mass and your get your impact in newtons. To convert newtons to pounds divided by 4.4