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An aeroplane is flying with velocity ve...

An aeroplane is flying with velocity ` vec v_p (= 100 ms^(-1)` towards East)
with respect to ground through motionless air and ` vec v_w` is the wind velocity with respect ot ground. The total velocity of aeroplane is ` vec v=vec v_P+ vec v_w`
The magnitude of the velocity is often called speed . the heading of the plane is the direction in which the nose of the plane is the direction is which th nose fo the plane points. In fact, it is the direction in which the engine propels the plane . Abswer the following questions :
If the wind blow with velocity ` 25 ms^(-1)` Norhtwards, the plane velocity is deflected from East by an angle.

A

` sin^(-1) (25//100)`

B

cos ^(-1) (25 //100)`

C

` tan^(-1) (25 //100)`

D

cot^(-1) ( 25 //100)`

Text Solution

Verified by Experts

The correct Answer is:
A
Refer to Gig. 2 (CF) . 74, as the resultant velocity is along ` OC`, so the plane velocity w.r.t ground must be along ` OB`, Here,
.
1 v_p = 100 ms^(-1) ` and ` v_w = 25 ms^)-1).
In ` Delta OCB`,
` sin phi = (CB)/(OB) = v_w /v_p = (25)/(100) or ` phi = sin^(-1) ((25)/(100))`.
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