Question

The pilot of an aircraft wishes to fly due west in a 41.0 km/h wind blowing toward the south. The speed of the aircraft relative to the air is 225 km/h.

(a) In what direction should the aircraft head?

(b)What will be its speed relative to the ground?

Answer 1

Solution) This problem is based on relative velocity

Here

Vw = 41km/h (south)

Va = 225km/h

(A) direction theeta=?

We have sin(theeta) = Vw/Va

Theeta = sine inverse(Vw/Va)

Theeta = asin(Vw/Va)

(In general sine inverse is represented as asin)

Theeta = asin(41/225) = 10.499° = 10.5°

So aircraft heads by theeta = 180° - 10.5° = 169.5°

So angle is 169.5°

(B) speed relative to ground ,Vg = ?

Vg = ((Va)^(2) - (Vw)^(2))^(1/2)

Vg = ((225)^(2) - (41)^(2))^(1/2)

Vg = 221.23 km/h