Question

$A$ moves with $65km/h$ while $B$ is coming back of $A$ with $80km/h$. The relative velocity of $B$ with respect to $A$ is

• A. $80km/h$
• B. $60km/h$
• C. $15km/h$
• D. $145km/h$

Answer 1

The correct option is D

$145km/h$

Step 1: Given Data:

Assuming the direction of A as negative,

Velocity of $\overrightarrow{V_A}=-65km/h$

Velocity of $\overrightarrow{V_B}=80km/h$

Since the velocity of $A$ and velocity of $B$are in the opposite direction. So, the velocity $A$ is taken as negative and the velocity of $B$ is taken as positive.

Step 2: Formula Used:

$\overrightarrow{V_{AB}}=\overrightarrow{V_A}-\overrightarrow{V_B}$

Where, $\overrightarrow{V_A}=$Velocity of $A$

$\overrightarrow{V_B}=$Velocity of $B$

$\overrightarrow{V_{AB}}=$Velocity of $A$ relative to $B$

Step 3: Calculating the relative velocity:

The velocity of $B$ relative to $A$,

$\overrightarrow{V_{BA}}=\overrightarrow{V_B}-\overrightarrow{V_A}$

$=80km/h-\left(-65km/h\right)$

$=145km/h$

Hence, option D is the correct answer.