SOLUTION: Atmospheric pressure P at an elevation of a feet above sea level is given by P=P0e-0.00004a Where P0 is the pressure at sea level,which is approximately 29.9 in inches of mercur

Question 237233: Atmospheric pressure P at an elevation of a feet above sea level is given by
P=P0e-0.00004a
Where P0 is the pressure at sea level,which is approximately 29.9 in inches of mercury(Hg).
Explain how a barometer, or some other device for measuring atmospheric pressure , can be used to find the height of a skyscraper.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
Equation would be:

P[a] =P[0] * e^(-0.00004*a)

* means multiply
^ means raise to the power of

a appears to be altitude
p[0] = 29.9 inches of mercury

p[a] would be the inches of mercury at an altitude of "a" feet.

since p[0] = 29.9 inches of mercury, we can replace p[0] in the equation with 29.9

assuming a = 0, then this equation would become:

p[0] = 29.9 * e^(-.00004*0)

this would become:

p[0] = 29.9 * e^0 which would become p[0] = 29.9 which would be correct since we would be at sea level.

if you were on a structure that was 1000 feet high, then this equation would become:

p[1000] = 29.9 * e^(-.00004*1000) which would become:

p[1000] = 29.9 * .960789439 which would become:

p[1000] = 28.72760423

If you want to measure the height of a building, all you have to do is go to the top of the building and measure the atmospheric pressure.

Once you have that, you can plug the value into the equation and solve for the height.

As an example:

Assume you go to the top of the building and you measure the atmospheric pressure to get:

atmospheric pressure at top of building = 27 inches of mercury.

your equation is:

p[a] = 29.9 * e^(-.00004*a)

Since you already know p[a], then you plug it into the equation to get:

27 = 29.9 * e^(-.00004*a)

divide both sides of this equation by 29.9 to get:

27/29.9 = e^(-.00004*a) which becomes:

.903010033 = e^(-.00004*a)

take the natural log of both sides of this equation to get:

ln(.903010033) = ln(e^(-.00004*a))

using the laws of logarithms, this equation becomes:

ln(.903010033) = ln(e) * (-.00004*a)

since ln(e) = 1, this equation becomes:

ln(.903010033) = -.00004*a

divide both sides of this equation by (-.00004) to get:

ln(.903010033)/(-.00004) = a

solve for a to get:

a = 2550.54036 feet.

the building would be approximately 2550 feet in height.

that's a very tall building, but that's only because I chose 27 inches of mercury at random without really knowing how high that would be.

in reality your measurement of atmospheric pressure would probably be around 28 or higher.

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