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Solution
We start by drawing position and vector diagrams where represents the velocity
of the wind and v ! w !
represents the velocity of the airplane in kilometres per hour.
NW
W
SW
N
S
NE
458
E
SE
w, )w ) = 100
458
v, )v ) = 400
w, )w ) = 100
458
v + w, resultant
v, )v ) = 400
Position diagram
Vector diagram
Use the cosine law to determine the magnitude of the resultant velocity.
0 v ! 0 v ! w !
w ! 0 2 0 v ! 0 2 0 w ! 0 2 2 0 v ! 00w ! 0 cos u, u 45°, 0 w ! 0 100, 0 v ! 0 400
0 2 400 2 100 2 21100214002cos 45°
0 v ! w ! 0 2 160 000 10 000 80 000 a 1 V2 b
0 v ! w ! 0 2 80 000
170 000
0 v ! w ! V2
0 336.80
To state the required velocity, the direction of the resultant vector is needed. Use
the sine law to calculate a, the angle between the velocity vector of the plane and
the resultant vector.
w, )w ) = 100
458
)v + w* = 336.80
a
v, )v ) = 400
sin a sin 45°
100 336.80
100sin 45°
sin a 0.2099
336.80
a 12.1°
Therefore, the resultant velocity is approximately
(or W77.9°N).
336.80 km>h, N12.1°W
366 7.2 VELOCITY
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