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

IN resultant direction `vecR`, the plane reaches the point B.

`Velocity of wing, vecV_m= 20 m/s`
` Velocity of aeroplane, V_a = 150 m/s`
In `/_\ACD,` according to sine formula
`:. 20/ (siN/A)= 150/(sin 30^0)`
`rarr sin A = 20/150 sin 30^0`
` = 20/150xx /2 = 1/15`
`rarr A= sin^-1 (1/15)`
`rarr A= sin^-1 (1/15)`
a The direction is `sin^-1 (1/15)` east of the line AB.
b. `sin^-1 1/15 = 3^0 48'`
`rarr 0^0+3^0 48' = 33^0 48'
`R=sqrt(150+20+2(150)20 cos (33^0 48'))`
` = sqrt(27886) = 167 m/s`
` time = S/v = 500000/167`
` = 2994 sec = 49.0 ~~ 50 min`.