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Occasionally, people can survive falling large distances if the surface they lan

ID: 1274564 • Letter: O

Question

Occasionally, people can survive falling large distances if the surface they land on is soft enough. During a traverse of Eiger's infamous Nordvand, mountaineer Carlos Ragone's rock anchor gave way and he plummeted 496 feet to land in snow. Amazingly, he suffered only a few bruises and a wrenched shoulder. Assuming that his impact left a hole in the snow 3.6 ft deep, estimate his average acceleration as he slowed to a stop Occasionally, people can survive falling large distances if the surface they land on is soft enough. During a traverse of Eiger's infamous Nordvand, mountaineer Carlos Ragone's rock anchor gave way and he plummeted 496 feet to land in snow. Amazingly, he suffered only a few bruises and a wrenched shoulder. Assuming that his impact left a hole in the snow 3.6 ft deep, estimate his average acceleration as he slowed to a stop

Explanation / Answer

481ft = 146.6088 m or lets call it 147m

5ft = 1.524m or lets call it 1.5m

for constant acceleration (we can assume that gravity is constant because 500ft is small system compared to size of planet) we can use

v=at

at 147m above snow, his velocity was zero, after falling to level of snow, his velocity increased exponentially

y = 0.5*at^2
so we can find time it took him to fall those 147m
t=sqrt(2*y/a)

y=147m
a=9.8m/s^2
t=5.477s

and he reached velocity

v=at = 53.68 m/s

then he had to decelerate through 1.5m of snow. when he stopped his velocity was zero but he sunk through d=1.5m of snow. assuming the deceleration was also constant, we can calculate time to stop

d=0.5*a*t^2
v=a*t

but this time "a" and "t" are different (a is larger value and opposite sign from gravity, time is shorter than those 5 or so seconds of plummeting from 147m) but starting velocity v in this portion of fall is same as final velocity of previous part (plummeting).

a=v/t

t=sqrt(2d/a)

a = v/(sqrt(2d/a)

a^2 = v^2/(2d/a)

a^2=av^2/(2d)

a=v^2/(2d)

a=53.68^2(2*1.5)=960.5 m/s^2

or a= 960.5 / 9.8 = 98g which is insane...

according to wiki, short 100g acceleration like in car crash is survivable