Relative velocity in two dimensions describes how an object moves when viewed from the perspective of another moving object, even if they are not moving in a straight line.

What is Relative Velocity?

Velocity is the speed of an object in a specific direction. When two objects are moving, we often want to know how fast one moves compared to the other. If you are sitting in a car moving at 50 km/h and pass another car moving at 40 km/h, the other car seems to move backward at only 10 km/h. This difference is relative velocity.

Moving in Two Dimensions

In two dimensions, objects can move sideways while also moving forward. We use coordinates, like x (horizontal) and y (vertical), to track this. If object A moves at velocity va and object B moves at velocity vb, the relative velocity of A with respect to B is written as vab = va - vb. Because these are vectors—quantities that have both size and direction—we must subtract the horizontal parts and vertical parts separately.

Real-World Example: Rain and Wind

Imagine you are running through rain that is falling straight down. To you, the rain seems to be hitting you at an angle. This happens because your horizontal velocity is combined with the vertical velocity of the raindrops. By using the relative velocity formula, you can calculate the exact angle at which you should hold your umbrella to stay dry while moving.

Key Steps for Calculations

• Identify the velocity vector of both objects (x and y parts).
• Subtract the x-component of the second object from the first.
• Subtract the y-component of the second object from the first.
• Use the Pythagorean theorem if you need the final speed (the magnitude of the vector).