Calculate the Relative Speed Between Two Airplanes

What is the magnitude of the relative speed between two airplanes?

Calculate the relative speed between two airplanes: one flying due east at 600 km/hr and the other flying in a heading 30 degrees west of north at 500 km/hr.

Answer:

The magnitude of the relative speed between the two airplanes is approximately 300.65 km/hr.

To calculate the magnitude of the relative speed between two airplanes, one flying due east at 600 km/hr and the other flying 30 degrees west of north at 500 km/hr, we can use vector addition.

The first airplane has a velocity vector pointing directly east (positive x-direction). Meanwhile, the second airplane's velocity vector is split into a northern component (positive y-direction) and a western component (negative x-direction).

To find the western component of the second airplane's velocity, we calculate 500 km/hr × cos(30), which gives us 433 km/hr west. For the northern component, we calculate 500 km/hr × sin(30), which gives us 250 km/hr north.

We can then calculate the relative speed by subtracting the x-components and combining them with the y-component (which remains unchanged) using the Pythagorean theorem: