An aeroplane has to go from a point A to another point B, 500 km away due 30° east of north. A wind is blowing due north at a speed of 20 m/s. The air speed of the plane is 150 m/s. (a) Find the direction in which the pilot should head the plane to reach the point B. (b) Find the time taken by the plane to go from A to B.Concept of Physics - 1 , HC VERMA , Chapter "Rest and Motion : Kinematics
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Solution :
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In resultant direction R , The plane reach the point B
Velocity of wind, Vm=20m/s
Velocity of aeroplane Va=150m/s
In the ΔACD,
Acording to sine formula:
20/SinA=150/Sin30°
Sin A=(20/150 )xsin30
=20/150 x1/2 =1/15
A= Sin⁻¹(1/15)
A) The direction is Sin⁻¹[1/15] to east of line AB.
b) Sin⁻¹1/15 =3°48
30°+3°433°48
R=√150+20+2(150)20cos(33°48)
=√27886
=167 m/s
time=s/v
time=500000/167
=2994 sec=49.9 min
∴The time taken by the plane to go from A to B is 49.9 min
**********************************
In resultant direction R , The plane reach the point B
Velocity of wind, Vm=20m/s
Velocity of aeroplane Va=150m/s
In the ΔACD,
Acording to sine formula:
20/SinA=150/Sin30°
Sin A=(20/150 )xsin30
=20/150 x1/2 =1/15
A= Sin⁻¹(1/15)
A) The direction is Sin⁻¹[1/15] to east of line AB.
b) Sin⁻¹1/15 =3°48
30°+3°433°48
R=√150+20+2(150)20cos(33°48)
=√27886
=167 m/s
time=s/v
time=500000/167
=2994 sec=49.9 min
∴The time taken by the plane to go from A to B is 49.9 min
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