# An airplane is flying at 200 km/h in a direction of 344 degrees. Find the westerly and northerly...

## Question:

An airplane is flying at 200 km/h in a direction of 344 degrees. Find the westerly and northerly components of its velocity.

## Vector Components

Certain quantities, such as velocity, are measured as a vector. This means that they have both a magnitude and a direction. We can separate a vector into its horizontal and vertical components by constructing a right triangle where the vector is the hypotenuse and the x and y axes are the horizontal and vertical components.

Before we can calculate the components of this plane's velocity, we need to understand what the angle of 344 degrees means. While in mathematics, we generally measure an angle counterclockwise from the positive x-axis. However, in practical applications, we usually measure an angle clockwise from north, so we'll use the latter to work through this problem.

Rather than work with such a large angle clockwise from north, let's worth with the corresponding angle measured counterclockwise, which is 360 minus this angle: 16 degrees west of north. If we make a right triangle with this being the angle we use in our calculations, then the hypotenuse has a value of 200, and x represents the horizontal component and y represents the vertical component of this velocity. We can use trigonometric ratios to find the values of x and y. The side adjacent to this angle is y, and the side opposite is x, so:

{eq}\cos 16^{\circ} = \frac{y}{200}\\ \rightarrow y= 200 \cos 16^{\circ} \approx 192.232\\ \sin 16^{\circ} = \frac{x}{200}\\ \rightarrow x = 200 \sin 16^{\circ} \approx 55.127 {/eq}

The vertical, or northerly component of this airplane's velocity is 192.232 kh/m, and the horizontal, or westerly component of this airplane's velocity is 55.127 km/r.