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?
- NCSLv 71 month agoFavourite 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
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
If you find this helpful, please select Favorite Answer. You get points too!