Question

An airplane with an airspeed of 600 km/h needs to be on a course 35.0 north of east. A steady wind of 100 km/h is blowing FROM the north. Determine the direction the plane should head.

Answer 1

Vp (vector velocity of the plane) = 600cos35i + 600sin35j

Vw (vector velocity of the wind) = -100j

The direction in which it should go is the direction of the velocity of the plane relative to the wind, Vpw

As a rule,

Vpw= Vp - Vw

=> Vpw= 491.5i + 344.1j + 100j = 491.5i + 444.1j

|Vpw|= 662.4 km/h (speed at which the plane heads, direction is given by tanA=j/i = 444.1/491.5)

tanA = 444.1/491.5

A = 42 degrees.

Therefore, the plane should head East 42 North.