Question

Example 3.72 An aeroplane has to go from a point O to another
due North at a speed of 10 ms. The air speed of the plane is
point A, at distance d due 37° East of North. A wind is blowing
to reach the point A. (ii) Find the time taken by the plane to go
v. (i) Find the direction in which the pilot should head the plane
The
from 0 to A
N
A
10 m/s
379 d
O
E
:) TC​

Answer 1

Explanation:

The vector diagram for various velocities is shown.Vector AC gives velocity of aeroplane relative to quiet air.Vector CB gives velocity of wind(air) relative to ground.Vector AB gives velocity of plane relative to ground.Using law of sines for triangle,

sin30

0

150

=

sinθ

20

.

Therefore,sin(θ)=

300

20

=

15

1

. Then,

Theta=sin

−1

15

1

=3.8

0

.

Angle NAC=33.8

0

.The pilot should head the plane in the direction 33.8

0

east of north