Chapter 4.2, Problem 41PPS

a.

To determine

To formulate the equation for barometric pressure

Answer to Problem 41PPS

  $B=-70a+724$

Explanation of Solution

Given:

Barometric pressure: 598 millimetres of mercury at altitude 1.8 kilometres

577 millimetres of mercury at 2.1 kilometres

Formula used:

Slope, $m=\frac{(y_2-y_1)}{(x_2-x_1)}$

Calculation:

Let x denote the altitude and y denote the barometric pressure.

Find the slope using the formula,

  $m=\frac{(y_2-y_1)}{(x_2-x_1)}$ where $\begin{array}{l}(x_1,y_1)=(1.8,598)\\ (x_2,y_2)=(2.1,577)\end{array}$

  $\begin{array}{l}\Rightarrow m=\frac{(577-598)}{(2.1-1.8)}=\frac{-21}{0.3}=-70\\ \end{array}$

Equation is slope-intercept form is $(y-y_1)=m(x-x_1)$

  $\begin{array}{l}\Rightarrow (y-598)=-70(x-1.8)\\ \Rightarrow y-598=-70x+126\\ \Rightarrow y=-70x+126+598\\ \Rightarrow y=-70x+724\end{array}$

Rewriting the above equation in terms of barometric pressure and altitude,

  $B=-70a+724$ where B is the barometric pressure and a is the altitude.

Conclusion:

Therefore, the formula for barometric pressure is $B=-70a+724$

b.

To determine

To calculate the altitude

Answer to Problem 41PPS

0.957

Explanation of Solution

Given:

From subpart (a),

  $B=-70a+724$

The barometric pressure is 657 millimetres of mercury.

Calculation:

From subpart (a),

  $B=-70a+724$ where B is the barometric pressure and a is the altitude.

Given that the barometric pressure is 657 millimetres of mercury,

Substituting above values in the equation,

  $\begin{array}{l}\Rightarrow 657=-70a+724\\ \Rightarrow 70a=724-657\\ \Rightarrow a=0.957\end{array}$

Conclusion:

Therefore, the altitude is 0.957.