Question

How do we calculate the relative velocities of two bicycles when one is still? When they are traveling in the same direction? When they are traveling in opposite directions? You might find it easier to answer if you randomly assign some numbers to each.

Answer 1

Relative velocity is defined as the velocity of a body compared to another.

( Or)

The difference between the velocities of body.

As the velocity is a vector, one must keep the direction into consideration as well.

Say,

Ther are two bodies A and B, moving with velocity V_A and V_B respectively.

Then, their relative velocity is written as

V_Relative = V_A ^_ V_B

Coming to the question, let's say the Velocities are V_A and V_B.

_{a) If one of the bicycle is still.}

If the bicycle B is still, it implies that its velocity, V_B=0

so Velocity of A w.r.t. B

V_Relative = V_A

b) If both bicycles are moving in same direction

Then Relative velocity of A w.r.t. B

V_Relative = V_A ^_ V_B

_{c) If both bicycles are moving in opposite direction}

_{Presume on direction to be positive axis, and other to be negative axis.}

_{So let's say, Bicycle A is moving in positive direction, and B in opposite direction of A}

Therefore, Relative velocity of A w.r.t. B

V_Relative = V_A _(_) V_B

= V_A + V_B

_Note: Please consider Vector sign above all V_A and V_B.

w.r.t. = with respect to.