# A plane has speed relative to air of 250 km/h. The displacement is 480 km [E 20 degree N].Wind is blowing at 40 km/h [E 30 degree N]?

A plane has speed relative to air of 250 km/h. The displacement is 480 km [E 20 degree N].Wind is blowing at 40 km/h [E 30 degree N]

a) In what direction should the pilot fly the plane?

b) How long does the trip take?

### 1 Answer

- NCSLv 71 month agoFavorite Answer
Vp/g = Vp/a + Va/g

where e.g."Vp/g" means "velocity of plane w/r/t ground"

for the east motion we can write

v*cos20 = 250*cosΘ + 40*cos30

where v is the speed of the plane relative to the ground.

0.940*v = 250*cosΘ + 34.64

for the north motion we have

v*sin20 = 250*sinΘ + 40*sin30

0.342*v = 250*sinΘ + 20

Two equations, two unknowns. Use any solution method you like. I use wolframalpha:

v = 289 km/h

and

Θ = 2 * 0.160567 * 180º/π rads = 18º N of E ◄

t = d / v = 480km / 289km/h = 1.66 hours,

or 1 hour 40 minutes

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