Afraid of Heights?

How much energy is absorbed by a person who hits the ground from a 10,000 meter drop?

Assume a mass of 45 kg and a terminal velocity of 200 km/h 200 \text{km/h} .

Enter your answer in joules rounded to the nearest hundred .


The answer is 69400.

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1 solution

John M.
Jun 7, 2015

Don't be.

This person , and some others throughout history, have survived such falls. This is truly incredible. Personally I thought there was no way. But as you can see, air can do a lot.

The force of air drag experienced by a falling object depends on the frontal area of the falling object - that is, on the amount of air the object must plow through as it falls - and on the speed of the falling object - the greater the speed, the greater the number of air molecules an object encounters per second and the greater the force of molecular impact. As a falling person gains speed, air drag may finally build up until it equals the weight of the skydiver. If and when this happens, the net force becomes zero and the person no longer accelerates; he/she has reached his/her terminal velocity (which takes about 20 seconds, practically - more than enough for the 10,000 meter drop).

Now of course if you land head-first you're done for. 70,000 Joules (derived from the kinetic energy at terminal velocity: E k = 1 2 m v t 2 E_k=\frac{1}{2}mv_t^2 ) of energy is the equivalent of about 150 expert karate punches distributed throughout your body. So landing makes a big difference. What also makes a difference is that the damage is not linear. You can have ten one-tenth of expert karate punches delivered to you, but they will nowhere near do as much damage as that single one. Same goes here.

But don't use this as an excuse to go skydiving without a parachute. You will probably lose enough IQ points to never solve a Brilliant problem again.

Here's a Wiki Guide on how to survive long falls - and free falls. Who knows. You may use it one day. Meanwhile,

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