What is the velocity at which an airplane must fly in order to cover the distance of 400 km to the north in 1 hour? If the wind is blowing to the north east (30° east of north) at 140 km/hr.
Solution. Posted on Friday, November 21, 2014.
The relative velocity law for two dimensions (non-relativistic) said that velocity of the object A relative to the non-moving object equal to the vector sum of the velocity of the object A relative to the object B and the velocity of the object B relative to the non-moving object.
V(airplane-Earth) = V(airplane-wind) + V(wind-Earth)
In order to solve this problem, let’s use the law of cosines .
c2 = a2 + b2 − 2ab cos(C)
V(airplane-wind)2 = 4002 + 1402 − 2*400*140*cos(30)
V(airplane-wind) = 287.41 km/hr
In order to find direction, let’s use the law of cosines again.
1402 = 287.412 + 4002 − 2*287.41*400*cos(C)
C= 14.10 West of North.