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# The pressure in the foothills of the Rockies near Boulder, Colorado is $84 ~\mathrm{kPa}$. The pressure, assuming a constant density of $1.00 ~\mathrm{~kg} / \mathrm{m}^3$, at the top of a nearby $4000$-$\mathrm{m}$-$\mathrm{high}$ mountain is closest to: (A) $60~ \mathrm{kPa}$ (B) $55 ~\mathrm{kPa}$ (C) $50 ~\mathrm{kPa}$ (D) $45 ~\mathrm{kPa}$

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We are asked to determine the estimated value of the pressure at the top of a $4000\,\text{m}$ mountain near the Rockies, which has pressure in its foothills of $84\,\text{kPa}$, considering a constant density.

We will determine the pressure on top of the nearby mountain specified in the problem using the following equation for the pressure difference between 2 points:

\begin{aligned} &dp=-\rho\cdot g\cdot dz\hspace{4.4cm}\tag1 \end{aligned}

where:

\begin{aligned} dp&=\text{pressure difference between 2 locations}\\ \rho&=\text{air density}\\ g&=\text{acceleration due to gravity}\\ dz&=\text{difference in elevation} \end{aligned}

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