Question

The barometer of a mountain hiker reads 750 mbars at the beginning of a hiking trip and 650 mbars at the end. Neglecting the effect of altitude on local gravitational acceleration, determine the vertical distance climbed. Assume an average air density of 1.35 kg/m3.

Answer 1

755.1 m

Step-by-step explanation:

Initial pressure = 750 mbar

Final pressure = 650 mbar

Converting to Pascal

1 mbar = 100 Pa

Initial pressure = 750 mbar = 75000 Pa

Final pressure = 650 mbar = 65000 Pa

ΔP = Pressure difference = 75000-65000 = 10000 Pa

g = Acceleration due to gravity = 9.81 m/s²

Δh = Height difference

ρ = Density of air = 1.35 kg/m³

ΔP = ρgΔh

`\Delta h=(\Delta P)/(\rho g)\\\Rightarrow \Delta h=(10000)/(1.35* 9.81)\\\Rightarrow \Delta h=755.1\ m`

∴ Vertical distance climbed is 755.1 m