IIT JEE , AIEEE Forum - Physics , Mechanics

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Let the plane head in a direction

North of East.
Let the velocity of the plane w.r.t be v_PW, the velocity of the wind wrt earth be v_WE & the velocity of the plane wrt earth be v_PEAlso, let the East direction be +X axis & the North direction be +Y axis.
Then,
v_{PE =}v_PW+v_WE= v_PW(sin

i + cos

j) + v_WE j = v_PWsin

i + (v_PWcos

+ v_WE )j
The plane should head along AB. So,
v_PWsin

/ (v_PWcos

+ v_WE )= tan30
150sin

/ (150cos

+ 20 ) = 1/

3
150(

3sin

- cos

) = 20
300sin(

-

/6 ) = 20

= sin^-1 (1/15) +

/6
Hence the angle made by the plane with the line AB ,

= (

-

/6 ) = sin^-1 (1/15)

Speed along AB = |v_PE| = v_PW cos

+ v_WEcos30 = 150

(1-1/15²) + 20 (

3/2)
= 40

14 + 10

3 m/s
Time taken to travel from A to B
=50000/(40

14 + 10

3) s

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