A plane flight 400 km West then 100 km what a plane flies 400 km West 100km not find its distance and bearing from it's starting point.

Answer 1

To find the distance and bearing from the starting point, we can use vector addition and trigonometry.

Let's denote the initial position as A, the first move as AB, and the second move as BC.

The displacement vector AB is 400 km West, which can be represented as (-400, 0) km.

The displacement vector BC is 100 km at an angle of 90 degrees (North), which can be represented as (0, 100) km.

Adding the two vectors together, we get the total displacement vector AC as (-400, 100) km.

Using the Pythagorean theorem, we can find the magnitude of vector AC:

|AC| = sqrt((-400)^2 + 100^2) = sqrt(160000 + 10000) = sqrt(170000) = 412.3 km

To find the bearing of point C from point A, we can use trigonometry:

tan(θ) = opposite/adjacent = 100/400
θ = tan^(-1)(0.25) ≈ 14.04 degrees

Therefore, the plane's distance from its starting point is 412.3 km and its bearing from the starting point is approximately 14.04 degrees.