The kilopascal is a unit of measure for atmospheric pressure. The atmospheric pressure at sea level is about 101 kilopascals. For every 1000-m increase in altitude, the pressure de... The kilopascal is a unit of measure for atmospheric pressure. The atmospheric pressure at sea level is about 101 kilopascals. For every 1000-m increase in altitude, the pressure decreases about 10.5%. What is the approximate pressure at an altitude of 3000 m?
Understand the Problem
The question asks to calculate the approximate atmospheric pressure at an altitude of 3000 meters, given that the pressure at sea level is 101 kilopascals and decreases by 10.5% for every 1000-meter increase in altitude. We need to apply the percentage decrease for each 1000-meter increment and then calculate the final pressure.
Answer
72 kilopascals
Answer for screen readers
72 kilopascals
Steps to Solve
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Calculate the pressure after the first 1000 meters The pressure decreases by 10.5% for every 1000 meters. So, we calculate the decrease in pressure after the first 1000 meters: $Decrease = 101 \times 0.105 = 10.605$ New Pressure $= 101 - 10.605 = 90.395$
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Calculate the pressure after the second 1000 meters Now, we need to calculate the pressure decrease from 1000 meters to 2000 meters using the new pressure: $Decrease = 90.395 \times 0.105 = 9.491475$ New Pressure $= 90.395 - 9.491475 = 80.903525$
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Calculate the pressure after the third 1000 meters Again, we calculate the pressure decrease from 2000 meters to 3000 meters: $Decrease = 80.903525 \times 0.105 = 8.494870125$ New Pressure $= 80.903525 - 8.494870125 = 72.408654875$
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Approximate the final pressure The approximate pressure at an altitude of 3000 meters is $72.408654875$ kilopascals. Rounding to the nearest whole number, we get 72 kilopascals.
72 kilopascals
More Information
The atmospheric pressure decreases exponentially with altitude. This is why the pressure decreases more at lower altitudes than at higher altitudes for the same 1000-meter increase.
Tips
A common mistake is to calculate the pressure decrease only once using the initial pressure at sea level and multiplying that decrease by 3. This would be incorrect because the pressure decreases based on the current pressure at each 1000-meter increment, not just the initial pressure. Another mistake is to not subtract the pressure decrease from the current pressure at each step.
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