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Question

An aero-plane pilot wishes to fly due west. A wind of 100 km/h is blowing toward the south. If the airspeed of the plane (its speed in still air) is 300 km/h, I which direction should the pilot head? What is the speed of the plane w.r.t. the ground?


A
θ=tan1(122)
vpg=2002m/s
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B

θ=tan1(1)

vpg=100m/s.

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C

θ=tan1(13)

vpg=300 m/s.

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D

θ=tan1(23)

vpg=2002m/s.

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Solution

The correct option is A θ=tan1(122)
vpg=2002m/s

GIven velocity of air with respect to ground vAG=100km/hr=100^j

Velocity of plane with respect to air vPA=300km/hr=300cosθ^i+300sinθ^j

(As the plane is to move towards west, due to air in south direction,air drift the plane in south direction.

Hence plane has to make an angle θ towards north-west direction, in order to reach at point on west.)

vPA=vPGvAGvPG=vPG+vAG=300 cosθ^i+300 sinθ^j+100^j

vPG=300 cos θ^i+(300 sinθ100)^j

We know that the plane has to go west wards and so the component of velocity towards north or in ^j

should be 0

300 sinθ100=0

sinθ=13

cosθ=223

tanθ=122

θ=tan1(122)

Direction heading of plane

vPG=300 cosθ^i(^j=0)

vPG=300×223

vPG=2002^i

So the plane will appear to be heading west with a velocity of 2002 m/s.


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