A wind blows at 100 km / h from the east. An aircraft points due north and sets off. In still air its speed is 150 km / h. What will the aircraft's actual velocity be?

180.28 km/h

Explanation:

Let north and south represent the positive and negative y axis and east and west represent the positive and negative x axis.

Given;

Velocity of wind vx= 100 km/s

Velocity of aircraft in still air vy = 150 km/s

The resultant velocity Vr is;

Vr = √(vx^2 + vy^2)

Vr = √(100^2 + 150^2)

Vr = 180.2775637731 km/h

Vr = 180.28 km/h

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west