Question

In some amazing situations, people have survived falling large distances when 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 512 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 4.8 ft deep, estimate his average acceleration as he slowed to a stop (that is while he was impacting the snow). Pick a coordinate system where down is positive.

Answer 1

Answer:

-3413 ft/s2

Explanation:

We need to know the velocity with which he landed on the snow.

He 'dropped' from 512 feet. This is the displacement. His initial velocity is 0 and the acceleration of gravity is 32 ft/s2.

We use the equation of mition

$v^2 = u^2 + 2as$

v and u are the initial and final velocities, a is the acceleration and s is the displacement. Putting the appropriate values

$v^2 = 0^2 + 2\times32\times512$

$v = \sqrt{2\times32\times512} = 128\sqrt{2}$

This is the final velocity of the fall and becomes the initial velocity as he goes into the snow.

In this second motion, his final velocity is 0 because he stops after a displacement of 4.8 ft. We use the same equation of motion but with different values. This time, $u=128\sqrt{2}$, v = 0 and s = 4.8 ft.

$0^2 = (128\sqrt{2})^2 + 2a\times4.8$

$a = -\dfrac{2\times128^2}{2\times4.8} = -3413$

Note that this is negative because it was a deceleration, that is, his velocity was decreasing.