An aeroplane has to go from a point A to another point B, `500 km` away due `30^@` east of north. 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.

Answer

A, B

Explanation

Applying sine law in `DeltaABC,` we have

`150/sin 30^@=v/sin theta=20/(sin(150-theta))`
From first and third we have,
`sin(150-theta)=(20 sin30^@)/150=1/15`
`:. 150-theta=sin^-1(1/15)`

Hence, we can see that direction of 150 m//s is
`150^@-theta[or sin^-1(1/15)]` east of the line AB
(b) `150^@-theta=sin^-1(1/15)=3.8^@`
`:. theta=146.2^@`
From first and second relation,
`v=(150sin theta)/sin 30^@`
Substituting the values we get,
`v=167 m//s`
`:. t=(AB)/v`
`=(500xx1000)/(167xx60) min=49.9 min`
`~~50 min`