Question

Assume a plane is flying directly north at 200 mph, but there is a wind blowing west at 23 mph. Part I: Express both the velocity of the plane and the velocity of the wind as vectors, using proper notation to represent each direction of motion. Part II: What is the velocity vector of the plane? Part III: What is the ground speed of the plane?

Answer 1

Define i  as a unit vector in the eastern direction.
Define j as a unit vector in the northern direction.

Part I
Because the wind is blowing west, its velocity vector is
 -23i mph or as (-23, 0) mph
Because the plane is traveling north, its velocity vector is
  200j mph or as (0, 200) mph 

Part II
The actual velocity of the plane is the vector sum of the plane and wind velocities.
That is,
200j - 23i or (-23, 200) mph

Part III
The ground speed of the plane is the magnitude of its vector.
The ground speed is
√[200² + (-23)²] = 201.32 mph

The ground speed of the plane is 201.3 mph (nearest tenth)

Not:
The direction of the plane is
 tan⁻¹ 23/200 = 6.56° west of north.