# The Speed and Direction of Two Planes

## What are the speeds and directions of the two planes?

1. Plane 1: 600 km/h, West

2. Plane 2: 667.0 km/h, Unknown direction

## Answer:

The first plane is flying at a speed of 600 km/h towards the west, while the second plane is flying at a speed of 667.0 km/h in an unknown direction.

To represent the speed and direction of the two planes, you can use vectors. The length of the vector signifies the speed, and the direction of the vector indicates the plane's velocity direction. For example, draw a left-facing arrow labeled '600 km/h, west' for the first plane and a longer arrow labeled '667.0 km/h, direction' for the second plane.

The pilot of the second plane employs a strategy to head somewhat east of north to compensate for wind velocity. By constructing a vector equation incorporating the plane's velocity relative to the ground and considering known velocities (plane's air velocity and wind velocity), you can determine the plane's velocity relative to the ground and the required heading angle.

Using unit vectors i and j to denote the positive directions on the x-axis and y-axis respectively aids in accurately representing the planes' velocities and directions. This detailed representation facilitates a better understanding of the planes' movements and strategies.