An aeroplane fles a straight path from town (A) to town ` B, 500 km` way . Town (B) is due East ot town (A) and a strong with blows from South to North at 1 300 km//h`. Tf the lane`s air speed is ` 900 km//h`. Which of following statements is true ?

Options

A. Trip time is ` 5 /6 sqrt 5 ) hour`
B. Plane's ground speed in ` 600 km//h`
C. Plane's heading is 30 degree South East.
D. plane' s heading is 60 degree south East.

Answer

A

Explanation

Refer to Fig. 2 (CF). 50. AB = 500 km.
.
Velocity of wind , ` v_w = 300 km//h` along ` AC`. The air plane can fly a st. path `AB` if the resultant velocity of aeroplane and with acts along ` AB`. It will be so it the velocity of aeroplane is represented by ` AD`.
V elocity along ` AB, ` v= sqrt (v_a^2 -v_w^2)`
` = sqrt ( 900^2 - 300 ^2 ) = sqrt ( 7200 ) = 600 sqr 2 km//h`
Time taken to reach ` B, t= S/v = ( 500 km )/(600 sqrt 2 km/h)`
` 5/( 6 sqrt 2)`
` sin theta = v_w /v_a = (300)/( 900) = 1/3 = 0 3333 = sin 19^2 28'`
` theta= 19^@ 28'`
` theta 19^@ 28' Suoth of East .