Relative velocity in two Dimensions – Class 11 | Chapter – 4 | Physics Short Notes Series PDF for NEET & JEE

Relative velocity in two Dimensions: Relative velocity in two dimensions refers to the velocity of an object as observed by an observer in a different reference frame. When dealing with two-dimensional motion, the relative velocity between two objects can be broken down into two components: a component parallel to the line joining the two objects, and a component perpendicular to this line.

Relative velocity in two Dimensions

Let’s consider two objects A and B moving in two dimensions. The velocity of object A relative to object B, denoted by v_AB, is given by:

v_AB = v_A – v_B

where v_A is the velocity of object A and v_B is the velocity of object B.

To find the component of the relative velocity parallel to the line joining the two objects, we can use the dot product of the relative velocity vector and a unit vector u in the direction of the line joining the two objects:

|v_AB| = v_AB · u

where the dot product is given by:

v_AB · u = |v_AB| |u| cos θ

and θ is the angle between the relative velocity vector and the unit vector u.

To find the component of the relative velocity perpendicular to the line joining the two objects, we can use the cross product of the relative velocity vector and a unit vector v perpendicular to the line joining the two objects:

v_AB⊥ = |v_AB × v|

where the magnitude of the cross product is given by:

|v_AB × v| = |v_AB| |v| sin θ

and θ is the angle between the relative velocity vector and the unit vector v.

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By Team Learning Mantras