Question

A moves with 65 km/hr while B is coming back from A with 80 km/hr. The relative velocity of B with respect to A is
A. 80 km/hr
B. 60 km/hr
C. 15 km/hr
D. 145 km/hr

Answer 1

Hint: To solve this question, first we know the basic concept of relative velocity. The relative velocity of two objects moving in same direction is \[|{{v}_{1}}+{{v}_{2}}|\] and the relative velocity of two objects moving in opposite direction is \[|{{v}_{1}}-{{v}_{2}}|\]. As the objects move in the opposite direction, the relative velocity is found by subtracting the two velocities and we find out the desired answer.

Formula Used:
${{v}_{AB}}={{v}_{A}}-{{v}_{B}}$
Where, ${{v}_{A}}$= velocity of A
${{v}_{B}}$= velocity of B
${{v}_{AB}}$= velocity of A relative to B

Complete step by step solution:
Given that A moves with 65 km/hr while B is coming back of A with 80 km/hr
We have to find out the relative velocity of B with respect to A
First we assume that the direction of A is negative.
Velocity of ${{v}_{A}}$= -65 km/hr
Velocity of ${{v}_{B}}$= 80 km/hr

Since the velocity of A and B are in opposite directions. So the velocity A is taken as negative and the velocity B is taken as positive. As we have to find the velocity of B with respect to A
${{v}_{BA}}$= ${{v}_{B}}$- ${{v}_{A}}$
$\Rightarrow {{v}_{BA}} = 80 – (-65)$
$\therefore {{v}_{BA}} = 145\,km/hr$
Hence, the velocity of B with respect to A is 145 km/hr.

Thus, option D is correct.

Note: Students must remember about the direction while forming the relative velocities and must take care in putting the negative and positive signs. Moreover, relative velocity is measured in relation to a reference point that is relative to a separate point, whereas velocity is measured with regard to a constant. As opposed to absolute velocity, which is measured in a frame where an object is either stationary or moving in comparison to it.