Question

An airplane has to fly eastward to adestination 856 km away. If wind is blowing at 18.0 m/s northwardand the air speed of the plane is 161 m/s, in what direction shoudthe plain head to reach its destination?
A. 6.42* south of east
B. 5.32* south of east
C. .11* south of east
D. 11.31* south of east

Answer 1

Explanation:

It is given that,

Distance between airplane and destination, d = 856 km

Speed of wind, $v_w=18\ m\s$

Speed of the airplane, $v_a=161\ m/s$

The vertical component of wind speed and speed of airplane is balanced so that the airplane moves eastward. So,

$161t\ sin\theta=18t$

on solving above equation,  

$\theta=sin^{-1}(\dfrac{18}{161})$

$\theta=6.419^{\circ}$

or

$\theta=6.42^{\circ}$ (south of east)

So, the plane is at 6.42 degrees south off eat. Hence, this is the required solution.