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## Homework Statement

During the second world war 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/in*.

^{2}Suppose that the lead plane 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 ft*, is it safe to drop the men?

^{2}## Homework Equations

I use two equations. One lead to the correct answer and that is the formula:

[tex]W=F\Delta x[/tex]

The other one lead to another answer and that is

[tex]v=\sqrt{2gh}[/tex]

## The Attempt at a Solution

I use the notation [tex]h=150 ft[/tex] [tex]m=144 lb[/tex] [tex]\Delta x = 2 ft[/tex] [tex]A=5ft^{2}[/tex]

**1.**The work done on the falling body is zero from jump to landing so [tex]0 = mgh-F\Delta x[/tex] and therefore [tex]F=\frac{mgh}{\Delta x}[/tex] The pressure is therefore [tex]P=\frac{F}{A}=\frac{mgh}{\Delta xA}= 15 lb/in^{2}[/tex]

**2.**The speed of the falling body at impact is [tex]v=\sqrt{2gh}[/tex] As it hits the snow it will drop in speed during a time [tex]\Delta t = \frac{\Delta x}{v}[/tex] Therefore the force on the body at landing will be [tex]F=\frac{mv}{\Delta t}[/tex] This leads to a pressure of [tex]P=\frac{mv}{\Delta t A}=\frac{2mgh}{\Delta x A} = 30 lb/in^{2}[/tex] Very risky indeed.

Now this is two answers and only one can be correct. What is wrong?