*An aircraft is to fly to a destination 800 km due north of its starting
point. Its airspeed is 800 km h−1. The wind is from the east at a speed
of 30 m s−1. On what compass heading should the pilot fly? How long
will the flight take? If the wind speed increases to 50 m s−1, and the
wind backs to the north-east, but no allowance is made for this change,
how far from its destination will the aircraft be at its expected arrival
time, and in what direction?
Answers
Answered by
2
Explanation:
Velocity of air (wind) = v
A
=100kmh
−1
Velocity of plane w.r.t. air = V
P/A
=300kmh
−1
v
→
P
=
v
→
P/A
+
v
→
A
The net velocity of the plane will be the vector sum of two velocities.
Velocity of air and velocity of plane w.r.t air. If the plane is to move towards west finally, then the N-S component of velocity should be zero. For this,
v
→
P/A
sinθ=v
A
⇒300sinθ=100
⇒sinθ=
3
1
⇒θ=sin
−1
(
3
1
)
So the pilot should head in direction θ=sin
−1
(
3
1
) N of W.
Speed of plane w.r.t ground,
v
P
=v
P/A
cosθ
=300
1−sin
2
θ
=300
1−(
3
1
)
2
=200
2
kmh
−1
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