Chapter 11.8, Problem 29PPS

(a)

To determine

To write: an equation for the total speed with a headwind and an equation for the total speed with a tailwind.

Answer to Problem 29PPS

The equation for the total speed with the tailwind is $s=r+w$

The equation for the total speed with the headwind is $s=r-w$

Explanation of Solution

Given:

Let $w$ be the speed of wind.

  $r$ be the speed set by the pilot.

  $s$ be the total speed.

Calculation:

Let $w$ be the speed of wind.

  $r$ be the speed set by the pilot.

  $s$ be the total speed.

The objective is to write an equation for the total speed with the headwind and an equation for the total speed with a tailwind.

The equation for the total speed with the headwind is calculated below.

  $s=r-w$

Therefore, the equation is $s=r-w$ .

The equation for the total speed with the tailwind is calculated below.

  $s=r+w$

Therefore, the equation is $s=r+w$

Conclusion:

The equation for the total speed with the tailwind is $s=r+w$

The equation for the total speed with the headwind is $s=r-w$

(b)

To determine

To write: a distance and time equation for a headwind and a tailwind.

Answer to Problem 29PPS

Distance equation for a headwind

  $\begin{array}{l}d=t\left(r-w\right)\\ \frac{d}{r-w}=t\end{array}$

Time equation for a tailwind:

  $\begin{array}{l}d=t\left(r+w\right)\\ \frac{d}{r+w}=t\end{array}$

Explanation of Solution

Calculation:

The distance formulas are as follows.

  $\begin{array}{l}d=t\left(r-w\right)\\ d=t\left(r+w\right)\end{array}$

The equation is solved for time is calculated below.

  $\begin{array}{l}d=t\left(r-w\right)\\ \frac{d}{r-w}=t\\ d=t\left(r+w\right)\\ \frac{d}{r+w}=t\end{array}$

Conclusion:

Therefore,

Distance equation for a headwind

  $\begin{array}{l}d=t\left(r-w\right)\\ \frac{d}{r-w}=t\end{array}$

Time equation for a tailwind:

  $\begin{array}{l}d=t\left(r+w\right)\\ \frac{d}{r+w}=t\end{array}$