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 stopExplanation / 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
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