# Relative Velocity Formula

Let us consider two bodies A and B which are moving relative to each other. The relative velocity is the velocity that the body A would appear to an observer on the body B and vice versa. Mathematically speaking the relative velocity is the vector difference between the velocities of two bodies.

Relative velocity = velocity of the body A – velocity of the body B

The equation is:

v_{AB} = v_{A} – v_{B}

Where:

v_{AB}: relative velocity of the body A respect body B

v_{A}: velocity of the body A

v_{B}: velocity of the body B

Relative Velocity Formula Questions:

1) An airplane A flies to the north with a velocity of 350 m/s. An airplane B flies to the south with a velocity of 500 m/s beside airplane A. Calculate:

a) The relative velocity to the airplane A respect airplane B

b) The relative velocity to the airplane A respect airplane B, but now both fly to the north

c) Compared the results

Answer:

We replace the data in the relative velocity equation:

a) v_{AB} = v_{A} – v_{B} = 350 m/s – (- 500 m/s) = 850 m/s

We considered the velocity of the airplane B as negative since it flies on opposite direction to the airplane A.

b) v_{AB} = v_{A} – v_{B} = 350 m/s – 500 m/s = 150 m/s

In this case we considered the velocity of the airplane B as positive because it flies in the same direction of the airplane A

c) For an observer on the airplane A in the first case, the relative velocity respect to the airplane B is higher compared to the second case, since they are moving away very fast, while in the second case they are approaching and.

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