Chapter 9.6, Problem 4OE

To determine

Tofind:the rate of plane with wind and against wind.

Answer to Problem 4OE

The rate of the plane with the wind is $\text{p+w}$ and the rate of the plane against wind is $\text{p-w}$ .

Explanation of Solution

Given:

  

Concept used:

If the plane is with the wind then it’s taken as $\text{+ive}\text{.}$

If the plane is against the windthen it’s taken as $\text{-ive}$ .

Vector formula:

  ${\text{R}}^2{\text{=A}}^{\text{2}}{\text{+B}}^{\text{2}}\text{+2ABcosθ}$ .

If the direction of plane is with the wind means planemakes ${\text{0}}^0$ with the wind.

The resultant will be:

  ${\text{R}}^2{\text{=A}}^{\text{2}}{\text{+B}}^{\text{2}}{\text{+2ABcos0}}^0$ .

  ${\text{R}}^2\text{=}{\left(\text{A+B}\right)}^2$ .

  $\text{R=}\left(\text{A+B}\right)$ .

Similarly,

If the direction of plane isagainst the wind means plane make ${\text{180}}^0$ with the wind.

  ${\text{R}}^2{\text{=A}}^{\text{2}}{\text{+B}}^{\text{2}}\text{-2AB}$ .

  $\text{R=A-B}$ .

  $\text{distance=rate}\times \text{time}$ .

Calculation:

If the rate of the plane in still air is $700$ and the rate of the wind is $50$ ,then

1.The rate of the plane with the wind is:

  $700+50=750$ .

The rate of the plane against wind is:

  $700-50=650$ .

If the rate of the plane in still air is $825$ and the rate of the wind is $100$ ,then

2.The rate of the plane with the wind is:

  $825+100=925$ .

The rate of the plane against wind is:

  $825-100=725$ .

If the rate of the plane in still air is $900$ and the rate of the wind is $\text{w}$ ,then

3.The rate of the plane with the wind is:

  $\text{900+w}$ .

The rate of the plane against wind is:

  $\text{900-w}$ .

If the rate of the plane in still air is $\text{p}$ and the rate of the wind is $\text{w}$ ,then

3.The rate of the plane with the wind is:

  $\text{p+w}$ .

The rate of the plane against wind is:

  $\text{p-w}$ .

Hence the table is

Rate of plane in still air	Rate of wind	Rate of plane with wind	Rate of plane against the wind
$700$	$50$	$\text{750}$	$\text{650}$
$825$	$100$	$\text{925}$	$\text{725}$
$900$	$\text{w}$	$\text{900+w}$	$\text{900-w}$
$\text{p}$	$\text{w}$	$\text{p+w}$	$\text{p-w}$

Hence, the rate of the plane with the wind is $\text{p+w}$ and the rate of the plane against wind is $\text{p-w}$ .