Question

Out of the two cars A and B, car A is moving towards east with a velocity of 10m/s whereas B is moving towards north with a velocity 20m/s, then velocity of A w.r.t B is (nearly)
(1) 30m/s
(2) 10m/s
(3) 22m/s
(4) 42m/s

Answer 1

Relative velocity is defined as the vector difference between the velocities of the two bodies with respect to each other. In order to find the solution of the given question write down all the provided physical quantities and then carefully apply the concept of relative velocity.
Formula Used: ${\vec v_{ab}} = {\vec v_a} + \vec v{}_b$

Complete answer:
Let us say that car A which is moving towards east is in positive X – direction, and car B which is moving towards north is in positive Y – direction.
The relative velocity of an object is defined as the velocity of an object B in the rest frame of another object A.
velocity of object B relative to A mathematically is given as,
${\vec v_{ab}} = {\vec v_a} + \vec v{}_b$
Now it is given that,
\eqalign{ & {V_a} = 10{\text{m/s \hat i}} \cr & {{\text{V}}_b} = 20{\text{m/s \hat i}} \cr}
So, velocity of car A with respect to car B is given as,
${\vec V_{ab}} = {\vec V_a} - {\vec V_b} = 10\hat i - 20\hat j$
\eqalign{ & |{{\vec V}_{ab}}| = \sqrt {{{\left( {10} \right)}^2} + {{\left( { - 20} \right)}^2}} = \sqrt {500} \cr & \therefore |{{\vec V}_{ab}}| = 10\sqrt 5 = 22.30{\text{m/s }} \approx {\text{22m/s}} \cr}
Thus, the velocity of A with respect to B nearly is 22 m/s.

Hence, option (3) is the correct answer.

Additional Information:
In physics, a frame of reference comprises an abstract system of coordinates and a set of physical reference points which uniquely fixes the coordinate system and standardizes the measurements within that frame of reference. Frame of reference is classified in two types, inertial frame of reference and non – inertial frame of reference. A frame of reference where Newton’s law holds true is known as an inertial frame of reference, whereas a frame of reference where Newton’s law does not hold true is known as a non – inertial frame of reference.

Note:
As we know all the motions are relative to some frame of reference. For example, when a body is at rest it means that it is not in motion. Which means that it is being described with reference to a frame of reference that is moving along the body.