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:
vAB = vA – vB
vAB: relative velocity of the body A respect body B
vA: velocity of the body A
vB: 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
We replace the data in the relative velocity equation:
a) vAB = vA – vB = 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) vAB = vA – vB = 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.