Pakistan's K2 is the world's second-tallest mountain, with an alt...

Question

Pakistan's K2 is the world's second-tallest mountain, with an altitude of 28,251 ft. Its base camp, where climbers stop to acclimate, is located about 16,400 ft above sea level.
(a) Approximate atmospheric pressure P at different altitudes is given by the equation P = e-h>7000, where P is in atmospheres and h is the altitude in meters. What is the approximate atmospheric pressure in mm Hg at K2 base camp?

Accepted Answer

Welcome back everyone. We're told that Mount fuji is approximately 12,389 ft above sea level. The standard hike up the mountain starts at 6600 ft. The atmospheric pressure at different altitudes can be approximated using the following equation where pressure is equal to Ulis number two, the negative power of height divided by 7000 where pressure is in atmospheres and height is in meters. We need to determine the atmospheric pressure in millimeters of mercury at the start of our hike and according to our prompt at the start of the hike, It's going to begin at a height of ft. Now, according to our equation, we know that height is in meters according to the prompt. And so we're going to convert from 6600 ft using strike geometry where feet will be in the denominator. And we're going to begin by going to units of inches. By recalling that we have for one ft and equivalent of 12 inches. We can now cancel out feet and focus on going from inches to centimeters By recalling that we have in one inch and equivalent of 2. centimeters, canceling out inches. We can now go from centimeters to meters And we're going to recall that we have 100 cm equivalent to one m. So canceling out cm were left with meters as our final unit for height. And this is going to yield the result of 2011. And let's make that an 11 there . m. So now we can go into the equation from the prompt to get pressure and we're going to plug in Mueller's number to the negative power of our height now which we just converted to meters. So we would have negative 2,011. m divided by 7000. And let's keep 7000 blue. So this is going to yield a pressure when we type this carefully into our calculators equal to .750-2. And recall that according to the prompt pressure is going to give us units of atmospheres here. Now, for our final answer, we want pressure to be in millimeters of mercury. So we're going to convert from a T. M's two millimeters of mercury by recalling that we have and will actually do the geometry here. So we're going to multiply by our conversion factor where from a T. M's two millimeters of mercury, we have an equivalent of 1 80 M equal to millimeters of mercury. So now we can cancel out a T M's. We're left with mm mm Mm HD as our final units. And this is going to yield a result of 570 of mercury as our final answer for the atmospheric pressure at the start of the hike. So this is our final answer. I hope what I went through was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video.

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