The barometer of a mountain hiker reads 930 mbars at the beginning of a hiking trip and 820 mbars at the end. Neglecting the effect of altitude on local gravitational acceleration, determine the vertical distance climbed. Assume an average air density of 1.20 kg/m3.
A mountain hiker reads 930 mbars at the beginning and 820 mbars finally in a barometer by climbing a mountain.A barometer is a scientific instrument used to measure the atmospheric pressure at a point.We need to find out the distance covered vertically by the climber.
At the beginning the pressure readed by the barometer is P bottom =(ρgh)bottom
P bottom =930 mbars
At the final point,(on the top) the pressure readed by the barometer P top =(ρgh)top
P top =820 mbars
Now consider an air column between the top and the bottom of the mountain .
The pressure of the air column can write as P air =(ρgh)air
We can write the pressure of the air column in terms of the pressure at the top of the mountain and bottom of the mountain as
P air =(P bottom - P top)
We have P air =(ρgh)air