Skip to main content
added 44 characters in body
Source Link
ACB
  • 2.6k
  • 2
  • 12
  • 36

@Señor O gives a very good answer, but he assumes an ideal deceleration. Based on a viewing of the scene, Anna sinks a little under a meter, while Kristoff doesn't sink more than half a meter.

Since they fell about 200 feet (about 60 m), my initial estimate for their impact velocity is (assuming no air resistance):

$v = \sqrt{2gh} = \sqrt{2*60*9.8} \approx 35 m/s$$v = \sqrt{2gh} = \sqrt{2*60*9.8} \approx 35 \ \mathrm{m/s}$

However, using a handy chart found in the resource below, when we factor in air resistance, Anna and Kristoff's impact velocity is actually around $33 m/s$$33 \ \mathrm{m/s}$

In Kristoff's case,

$v^2 = v_o^2 + 2a\Delta x$

$1100 = 2(0.5)a$

$1100 m/s^2 = a$$1100\ \mathrm{ m/s^2} = a$

which is about $110g$. Possibly fatal, especially considering that the way he lands would cause severe stress on the spinal cord.

In Anna's case,

$1100 = 2(1)a$

$550m/s^2 = a$$550\ \mathrm{m/s^2 }= a$

which is about $55g$. Probably survivable, (some car crashes experience higher gs), but would likely injure her. She does land feet-first (probably the optimal way to land in this case), which would prevent some injury. In short, the duo might survive, but they would not be able to just get up and continue on their merry way.

This FAA paper is my primary source for my calculations.

@Señor O gives a very good answer, but he assumes an ideal deceleration. Based on a viewing of the scene, Anna sinks a little under a meter, while Kristoff doesn't sink more than half a meter.

Since they fell about 200 feet (about 60 m), my initial estimate for their impact velocity is (assuming no air resistance):

$v = \sqrt{2gh} = \sqrt{2*60*9.8} \approx 35 m/s$

However, using a handy chart found in the resource below, when we factor in air resistance, Anna and Kristoff's impact velocity is actually around $33 m/s$

In Kristoff's case,

$v^2 = v_o^2 + 2a\Delta x$

$1100 = 2(0.5)a$

$1100 m/s^2 = a$

which is about $110g$. Possibly fatal, especially considering that the way he lands would cause severe stress on the spinal cord.

In Anna's case,

$1100 = 2(1)a$

$550m/s^2 = a$

which is about $55g$. Probably survivable, (some car crashes experience higher gs), but would likely injure her. She does land feet-first (probably the optimal way to land in this case), which would prevent some injury. In short, the duo might survive, but they would not be able to just get up and continue on their merry way.

This FAA paper is my primary source for my calculations.

@Señor O gives a very good answer, but he assumes an ideal deceleration. Based on a viewing of the scene, Anna sinks a little under a meter, while Kristoff doesn't sink more than half a meter.

Since they fell about 200 feet (about 60 m), my initial estimate for their impact velocity is (assuming no air resistance):

$v = \sqrt{2gh} = \sqrt{2*60*9.8} \approx 35 \ \mathrm{m/s}$

However, using a handy chart found in the resource below, when we factor in air resistance, Anna and Kristoff's impact velocity is actually around $33 \ \mathrm{m/s}$

In Kristoff's case,

$v^2 = v_o^2 + 2a\Delta x$

$1100 = 2(0.5)a$

$1100\ \mathrm{ m/s^2} = a$

which is about $110g$. Possibly fatal, especially considering that the way he lands would cause severe stress on the spinal cord.

In Anna's case,

$1100 = 2(1)a$

$550\ \mathrm{m/s^2 }= a$

which is about $55g$. Probably survivable, (some car crashes experience higher gs), but would likely injure her. She does land feet-first (probably the optimal way to land in this case), which would prevent some injury. In short, the duo might survive, but they would not be able to just get up and continue on their merry way.

This FAA paper is my primary source for my calculations.

updated info considering air resistance
Source Link
Dave Coffman
  • 1.5k
  • 14
  • 22

@Señor O gives a very good answer, but he assumes an ideal deceleration. Based on a viewing of the scene, Anna sinks a little under a meter, while Kristoff doesn't sink more than half a meter.

Since they fell about 200 feet (about 60 m), my initial estimate for their impact velocity is (assuming no air resistance):

$v = \sqrt{2gh} = \sqrt{2*60*9.8} \approx 35 m/s$

However, using a handy chart found in the resource below, when we factor in air resistance, Anna and Kristoff's impact velocity is actually around $33 m/s$

In Kristoff's case,

$v^2 = v_o^2 + 2a\Delta x$

$1200 = 2(0.5)a$$1100 = 2(0.5)a$

$1200 m/s^2 = a$$1100 m/s^2 = a$

which is about $120g$$110g$. Possibly fatal, especially considering that the way he lands would cause severe stress on the spinal cord.

In Anna's case,

$1200 = 2(1)a$$1100 = 2(1)a$

$600m/s^2 = a$$550m/s^2 = a$

which is about $60g$$55g$. Probably survivable, (some car crashes experience higher gs), but would likely injure her. She does land feet-first, which is better than Kristoff (probably the optimal way to land in this case), which would preventprevent some injury. In short, the duo might survive, but they would not be able to just get up and continue on their merry way.

Here'sThis a link to a very informativeFAA paper on impact survivabilityis my primary source for humansmy calculations.

@Señor O gives a very good answer, but he assumes an ideal deceleration. Based on a viewing of the scene, Anna sinks a little under a meter, while Kristoff doesn't sink more than half a meter.

Since they fell about 200 feet (about 60 m), their impact velocity is (assuming no air resistance):

$v = \sqrt{2gh} = \sqrt{2*60*9.8} \approx 35 m/s$

In Kristoff's case,

$v^2 = v_o^2 + 2a\Delta x$

$1200 = 2(0.5)a$

$1200 m/s^2 = a$

which is about $120g$. Possibly fatal, especially considering that the way he lands would cause severe stress on the spinal cord.

In Anna's case,

$1200 = 2(1)a$

$600m/s^2 = a$

which is about $60g$. Probably survivable, (some car crashes experience higher gs), but would likely injure her. She does land feet-first, which is better than Kristoff, which would prevent some injury. In short, the duo might survive, but they would not be able to just get up and continue on their merry way.

Here's a link to a very informative paper on impact survivability for humans.

@Señor O gives a very good answer, but he assumes an ideal deceleration. Based on a viewing of the scene, Anna sinks a little under a meter, while Kristoff doesn't sink more than half a meter.

Since they fell about 200 feet (about 60 m), my initial estimate for their impact velocity is (assuming no air resistance):

$v = \sqrt{2gh} = \sqrt{2*60*9.8} \approx 35 m/s$

However, using a handy chart found in the resource below, when we factor in air resistance, Anna and Kristoff's impact velocity is actually around $33 m/s$

In Kristoff's case,

$v^2 = v_o^2 + 2a\Delta x$

$1100 = 2(0.5)a$

$1100 m/s^2 = a$

which is about $110g$. Possibly fatal, especially considering that the way he lands would cause severe stress on the spinal cord.

In Anna's case,

$1100 = 2(1)a$

$550m/s^2 = a$

which is about $55g$. Probably survivable, (some car crashes experience higher gs), but would likely injure her. She does land feet-first (probably the optimal way to land in this case), which would prevent some injury. In short, the duo might survive, but they would not be able to just get up and continue on their merry way.

This FAA paper is my primary source for my calculations.

prep for drag addition
Source Link
Dave Coffman
  • 1.5k
  • 14
  • 22

@Señor O gives a very good answer, but he assumes an ideal deceleration. Based on a viewing of the scene, Anna sinks a little under a meter, while Kristoff doesn't sink more than half a meter.

Since they fell about 200 feet (about 60 m), their impact velocity is (assuming no air resistance):

$v = \sqrt{2gh} = \sqrt{2*60*9.8} \approx 35 m/s$

In Kristoff's case,

$v^2 = v_o^2 + 2a\Delta x$

$1200 = 2(0.5)a$

$1200 m/s^2 = a$

which is about $120g$. Possibly fatal, especially considering that the way he lands would cause severe stress on the spinal cord.

In Anna's case,

$1200 = 2(1)a$

$600m/s^2 = a$

which is about $60g$. Probably survivable, (some car crashes experience higher gs), but would likely injure her. She does land feet-first, which is better than Kristoff, which would prevent some injury. In short, the duo might survive, but they would not be able to just get up and continue on their merry way.

Here's a link to a very informative paper on impact survivability for humans.

@Señor O gives a very good answer, but he assumes an ideal deceleration. Based on a viewing of the scene, Anna sinks a little under a meter, while Kristoff doesn't sink more than half a meter.

Since they fell about 200 feet (about 60 m), their impact velocity is

$v = \sqrt{2gh} = \sqrt{2*60*9.8} \approx 35 m/s$

In Kristoff's case,

$v^2 = v_o^2 + 2a\Delta x$

$1200 = 2(0.5)a$

$1200 m/s^2 = a$

which is about $120g$. Possibly fatal, especially considering that the way he lands would cause severe stress on the spinal cord.

In Anna's case,

$1200 = 2(1)a$

$600m/s^2 = a$

which is about $60g$. Probably survivable, (some car crashes experience higher gs), but would likely injure her. She does land feet-first, which is better than Kristoff, which would prevent some injury. In short, the duo might survive, but they would not be able to just get up and continue on their merry way.

Here's a link to a very informative paper on impact survivability for humans.

@Señor O gives a very good answer, but he assumes an ideal deceleration. Based on a viewing of the scene, Anna sinks a little under a meter, while Kristoff doesn't sink more than half a meter.

Since they fell about 200 feet (about 60 m), their impact velocity is (assuming no air resistance):

$v = \sqrt{2gh} = \sqrt{2*60*9.8} \approx 35 m/s$

In Kristoff's case,

$v^2 = v_o^2 + 2a\Delta x$

$1200 = 2(0.5)a$

$1200 m/s^2 = a$

which is about $120g$. Possibly fatal, especially considering that the way he lands would cause severe stress on the spinal cord.

In Anna's case,

$1200 = 2(1)a$

$600m/s^2 = a$

which is about $60g$. Probably survivable, (some car crashes experience higher gs), but would likely injure her. She does land feet-first, which is better than Kristoff, which would prevent some injury. In short, the duo might survive, but they would not be able to just get up and continue on their merry way.

Here's a link to a very informative paper on impact survivability for humans.

fixed some inaccurate initial assumptions
Source Link
Dave Coffman
  • 1.5k
  • 14
  • 22
Loading
added 10 characters in body
Source Link
Dave Coffman
  • 1.5k
  • 14
  • 22
Loading
Source Link
Dave Coffman
  • 1.5k
  • 14
  • 22
Loading