Question

What are the speeds of two objects if, when they move uniformly towards each other, they get $6m$ closer in each second and when they move uniformly in the same direction with the original speeds, they get $6.0m$ closer in each $10s$?

• A. $3.3m/s$ and $1.2m/s$
• B. $5.2m/s$ and $4.6m/s$
• C. $3m/s$ and $3m/s$
• D. $3.3m/s$ and $2.7m/s$

Answer 1

The correct option is D $3.3m/s$ and $2.7m/s$

Let $\overrightarrow{V_A}$ and $\overrightarrow{V_B}$ be the velocities of two objects moving uniformly.
Case 1: When objects are moving opposite to each other:
In this case the relative speed of object $A$ w.r.t object $B$ is given by $V_{AB}=V_A-(-V_B)$ (∵$\overrightarrow{V_A}$ is in the opposite direction to that of object $\overrightarrow{V_B}$)
⟹$V_{AB}=V_A+V_B$
According to question :$(V_A+V_B)\times 1s=6m$
⟹$V_A+V_B=6m/s$ (i)
Case 2: When objects are moving in same direction.
In this case the relative speed of object $A$ w.r.t object $B$ is given by $V_{AB}=V_A-V_B$
According to question:
$(V_A-V_B)\times 10s=6m$
⟹$(V_A-V_B)=0.6m/s$ (ii)
Using (i) and (ii) we get $V_A=3.3m/s$ and $V_B=2.7m/s$