# On the map, let the +x-axis point east and the +y-axis north. An airplane flies at 810 km/h in...

## Question:

On the map, let the +x-axis point east and the +y-axis north. An airplane flies at 810 km/h in the south direction. Enter the x and y components of the velocity separated by a comma.

## Vector Components:

The direction of a vector has an effect on the projection of the vector itself onto any of the coordinate axes. These projections are called "components". If we are given an angle with respect to a reference point as the direction of a vector, we can use trigonometric identities in order to determine each axis component of a vector.

If the +x-axis is east and the +y-axis is north, then this means that the opposite must also true: the -x-axis is west and the -y-axis is south. Since our airplane is flying south, this means that it is only moving along the {eq}\displaystyle \rm \pm y {/eq} axis and it does not have a component along the {eq}\displaystyle \rm \pm x {/eq} axis at all. Therefore, our x- and y-components are:

{eq}\displaystyle \rm \boxed{\rm [v_x, v_y] = [0, -810\ km/h]} {/eq}

The negative sign denotes that the direction of the plane is along the -y-axis.