Chapter 5, Problem 5STP

To determine

To Choose: The correct option.

Answer to Problem 5STP

Option B

Explanation of Solution

Given:

Velocity of airplane, $v_p=800.0\text{km/h}$ Eastwards

Velocity of wind, $v_w=80.0\text{km/h}$ From South-west towards North-East

Formula Used:

Resultant velocity:

  $v=\sqrt{v_1{}^2+v_2{}^2+2v_1{v}_2\cos \theta }$

Where, $\theta$ is the angle between two velocities.

Direction of the resultant velocity can be obtained by:

  $\alpha ={\tan }^{-1}\left(\frac{v_2\sin \theta }{v_1+v_2\cos \theta }\right)$

Calculation:

  $\theta =45°$

  $\begin{array}{c}v=\sqrt{v_1{}^2+v_2{}^2+2v_1{v}_2\cos \theta }\\ =\sqrt{{800.0}^2+{80.0}^2+2\left(800.0\right)\left(80.0\right)\cos 45°}\\ =\sqrt{69.28}\\ =858\text{km/h}\end{array}$

  $\begin{array}{c}\alpha ={\tan }^{-1}\left(\frac{80.0\sin 45°}{800.0+80.0\cos 45°}\right)\\ ={\tan }^{-1}\left(0.06\right)\\ =3.8°\end{array}$

Conclusion:

Thus, the correct option is B.