Question

A ship is travelling North with a speed of 40km/h with a flag on its mast. If wind starts blowing with a velocity 30km/h from East to West direction, then the flag will flutter in direction:
A). 37° South of West
B). 53° West of North
C). 37° West of South
D). 53° East of North​

Answer 1

Given:

A ship is travelling due North with a speed of 40km/h with a flag on its mast. Wind starts blowing with a velocity 30km/h from East to West direction.

To find:

Direction in which the flag will flutter.

Calculation:

First, refer to the attached diagram which involves the vectors.

Let velocity of ship be v_(s) and wind velocity be v_(w).

$\sf{v_{resultant} = \sqrt{ {30}^{2} + {40}^{2} } }$

$\sf{ = > v_{resultant} = \sqrt{ {50}^{2} } }$

$\sf{ = > v_{resultant} = 50 \: km {hr}^{ - 1} }$

$\rm{ \therefore \cos( \theta) = \dfrac{40}{50} }$

$\rm{ = > \cos( \theta) = \dfrac{4}{5} }$

$\rm{= > \: \theta = 37 \degree}$

So, the flag will flutter in a direction 37° west of south.