Question

When two objects move uniformly towards each other, they get $4\text{m}$ closer in each second and when they move uniformly in the same direction with the original speeds, they get $4.0\text{m}$ closer in each $10\text{s}$. What are the speed of the objects?

• A. $2.8\text{m/s}$ and $1.2\text{m/s}$
• B. $5.2\text{m/s}$ and $4.6\text{m/s}$
• C. $32\text{m/s}$ and $2.1\text{m/s}$
• D. $2.2\text{m/s}$ and $1.8\text{m/s}$

Answer 1

The correct option is D $2.2\text{m/s}$ and $1.8\text{m/s}$

Let $V_A$ and $V_B$ be the velocities of two objects moving uniformly.
Case 1:
When objects are moving towards each other
In this case the relative velocity of object $A$ w.r.t object $B$ is given by
$V_{AB}=V_A-(-V_B)$
($\because V_B$ is in the opposite direction to that of object $A$)
$V_{AB}=V_A+V_B$
According to question
$(V_A+V_B)\times 1\text{s}=4\text{m}$
$\Rightarrow V_A+V_B=4\text{m/s}$ ... (i)
Case 2:
When objects are moving in same direction
In this case the relative velocity of object $A$ w.r.t object $B$ is given by
$V_{AB}=V_A-V_B$
According to question
$(V_A-V_B)\times 10\text{s}=4\text{m}$
$\Rightarrow (V_A-V_B)=0.4\text{m/s}$ ... (ii)
Using (i) and (ii) we get
$V_A=2.2\text{m/s}$
and $V_B=1.8\text{m/s}$