Deceleration of a man falling off a cliff into snow

In summary, the problem involves calculating the depth a man would be buried in soft snow after falling off a cliff of 37.8 m and landing on his back with a constant deceleration of 100 g's. Using the SUVAT equations of motion, the time it takes for the man to fall is 2.78 seconds and his final velocity is 27.2 m/s. However, when trying to calculate the time and distance in the snow portion, there seems to be some discrepancy. Other equations of motion can also be used to solve this problem.
  • #1
salmayoussef
31
0

Homework Statement



A person can just survive a full-body collision (either to the front, back, or side) which results in a deceleration that is up about 100 g's. (One g is 9.8 m/s/s). At greater deceleration fatal brain damage will likely occur. If a 66.4 kg man falls of a cliff of height 37.8 m but manages to land flat on his back in soft snow, undergoing a constant deceleration of this magnitude, how deep would he be buried in the snow?

I feel like this is very simple and I'm just over thinking it...

dy = 37.8 m
g = -980 m/s2

(Not sure about g...)

Homework Equations



Possibly one of the constant acceleration equations (not sure which).

The Attempt at a Solution



I tried to think about it as if the man was a car driving horizontally then suddenly begins to decelerate, then tried to find his distance after he breaks. No luck. I still can't figure it out... Any advice would be appreciated! :)
 
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  • #2
salmayoussef said:
g = -980 m/s2

(Not sure about g...)
Why would you be "not sure"? In the problem it says "(One g is 9.8 m/s/s)"

You know that v= gt where v is the speed after t seconds and d= (g/2)t^2 where d is the distance traveled in t seconds. How long will it take to fall 37.8 m? (I assume that is the distance to the top of the snowbank.) What will his speed be at that point (as he hits the snow bank).

At -100g= -980 m/s^2 (was that what you meant, not "g= -980 m/s2"?) how long will it take for him to stop (his speed to become 0)? And how far will he have gone through the snow in that time?
 
  • #3
Well, I tried it out using d = 0.5gt2 and found that the time is 2.78 s.

Then using time, I found that the final velocity was 27.2 m/s. (v = gt)

Then for the snow portion, I tried to find time using the same equation and got 0.028 s which I don't think is right. Waaaaay too fast!

And finally, I used d = 0.5(Vf+Vi)t to find that d = 0.38 m. But it isn't the proper answer! Any advice?
 
  • #4
salmayoussef said:
Well, I tried it out using d = 0.5gt2 and found that the time is 2.78 s.

Then using time, I found that the final velocity was 27.2 m/s. (v = gt)

Then for the snow portion, I tried to find time using the same equation and got 0.028 s which I don't think is right. Waaaaay too fast!
Show your working so we can see where you may be going wrong. Or confirm that you're right.
 
  • #5
The equation d = 0.5gt^2 looks like a variant of the SUVAT equations of motion. This problem is mostly about distance and velocity so why use one that involves time? That's not the wrong approach but it might be worth you looking at some of the others.

http://en.wikipedia.org/wiki/Equations_of_motion#SUVAT_equations
 

1. How does the deceleration of a man falling off a cliff into snow compare to falling onto a hard surface?

The deceleration of a man falling into snow is generally less severe than falling onto a hard surface. This is because the snow acts as a cushion, absorbing some of the impact and slowing down the person's descent.

2. What factors affect the deceleration of a man falling into snow?

The main factors that affect the deceleration of a man falling into snow are the depth and density of the snow, as well as the angle and speed at which the person falls. Deeper and denser snow will provide more cushioning, while a steeper angle and higher speed will result in a greater deceleration.

3. How does the weight of the person falling affect their deceleration into snow?

The weight of the person falling does have an impact on their deceleration into snow. A heavier person will typically experience a greater deceleration, as they will apply more force to the snow upon impact.

4. What role does air resistance play in the deceleration of a man falling into snow?

Air resistance can play a small role in the deceleration of a man falling into snow, as the air molecules will slow down the person's descent slightly. However, the effect of air resistance is much less significant than the impact of hitting the snow itself.

5. Can the deceleration of a man falling into snow be predicted or controlled?

The deceleration of a man falling into snow can be estimated using physics principles and equations. However, it is difficult to accurately predict or control as it depends on various factors, such as the individual's body position and the condition of the snow. It is important to take proper precautions and avoid falling from high heights to minimize the risk of injury from deceleration into snow.

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