An airplane flies at airspeed (relative to the

Question

air) of 250 km/h. The pilot wishes to fly due
North (relative to the ground) but there is a
55 km/h wind blowing Southwest (direction
225◦).
In what direction should the pilot head the
plane (measured clockwise from North)?
Answer in units of ◦.

Answer 1

the 55 kph SW wind has a W component of magnitude ... 55 sin(45º)

the plane needs to fly N , with an E component of similar magnitude

the sine of the direction angle is ... [55 sin(45º)] / 250

Answer 2

Vr = Vp + 55km/h[225o] = 250,
Vp + 55*sin225 + (55*cos225)I = 250,
Vp - 38.9 - 38.9i = 250,
Vp = 88.9 + 38.9i = 97km/h[66.4o] CW.
Direction = 66.4o CW.

Answer 3

Correction: Last step, Vp = 288.9 + 38.9i = 292.5km/h[82.3o] CW.
Direction = 82.3o CW.

Answer 4

henry2

the plane flies at 250 kph
... it has to compensate for an approximate 40 kph west wind
... both of your solutions are WAY off the mark

stop confusing students

Answer 5

The vector sum of plane and wind should be 250 km/h due north:
Check: (288.9+38.9i) + (-38.9-38.9i) = 250 km/h.