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## Homework Statement

During World War II the Russians, lacking sufficient

parachutes for airborne operations, occasionally dropped soldiers

inside bales of hay onto snow.

The human body can survive an average pressure on impact of

30 lb/in2 . Suppose that the lead plane drops a dummy bale equal

in weight to a loaded one from an altitude of 150 ft, and that the

pilot observes that it sinks about 2 ft into the snow. If the weight of

an average soldier is 144 lb and his effective area is 5 ft2 , is it safe

to drop the men?

## Homework Equations

energy conservation

## The Attempt at a Solution

For clarity, I set h1 = 150ft, h2 = 2ft, mg = 144lb, and S = 5lb/ft^2.

Using conservation of energy, the paratrooper's speed just before impact is ##v_i = \sqrt{2gh_1}##.

If ## E_r## is the mechanical energy once the paratrooper is at rest 2ft under snow, ##E_i## the mechanical energy at impact, and ##\vec N## the force of snow on man, then:

##

\left\{

\begin{array}{}

E_r = 0\\

E_i = mg (h_1+h_2) \\

E_r - E_i = \int_{\vec r_{impact}}^{\vec r_{rest}} \vec N.d\vec r

\end{array}

\right.

##

And, because the force of the snow is vertical,

## mg(h_1+h_2) = \int_{0}^{h_2} N(y) dy \approx h_2 N_{av} ##

So the average pressure the paratrooper must resist is

##\frac{N_{av}}{S} = 144*152/(2*5) \ lb/ft^2 = 152/(2*5) \ lb/in^2 = 15.2 \ lb/in^2 < 30 \ lb/in^2##

So yes it is 'safe' (non lethal). Is it correct ?

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