Chapter 8.7, Problem 7CYU

To determine

To calculation:

Resultant velocity and direction of plane.

Answer to Problem 7CYU

The plane would be traveling at about $109.9milesperhour$ at an angle of about $7.3$ .

Explanation of Solution

Given information:

  

Calculation:

For finding out velocity and direction of plane, initially component form of the planes vector,

  $\begin{array}{l}\cos 8°=\frac{x}{100}\\ x=100.\cos 8°\approx 99.03\\ \sin 8°=\frac{y}{100}\\ y=100.\sin 8°\approx 13.92\end{array}$

The planes vector is $\langle 99.03,13.92\rangle$

Since the wind is parallel to the ground its $y$ component is zero.

The wind vector is $\langle 10,0\rangle$

Add the planes vector with winds vector.

  $\begin{array}{l}\langle 99.03+10,13,92+0\rangle \\ \langle 109.03,13.92\rangle \end{array}$

Now use Pythagoras theorem to find the resulting vector magnitude.

  $\begin{array}{l}m=\sqrt{{109.03}^3+{13.92}^2}\\ m=109.92m/h\end{array}$

To find vector direction use trigonometry,

  $\begin{array}{l}\tan \theta =\frac{opp}{adj}\\ \tan a=\frac{13.92}{109.03}\\ a={\tan }^{-1}\left(\frac{13.92}{109.03}\right)\\ a=7.3\end{array}$

Hence, the plane would be traveling at about $109.9milesperhour$ at an angle of about $7.3$ .