Question 237233
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.