Question

Two cars are moving in the same direction with the same speed 30 km/hr. They are separated by a distance of 5 km, the speed of a car moving in the opposite direction if it meets these two cars at an interval of 4 minutes, will be

• A. $40km/hr$
• B. $45km/hr$
• C. $30km/hr$
• D. $15km/hr$

Answer 1

Answer: (B)

$45km/hr$

The two car (say $A$ and $B$) are moving with same velocity, the relative velocity of one (say $B$) with respect to the other
$A,{\overrightarrow{V}}_{B}A={\overrightarrow{V}}_B-{\overrightarrow{V}}_A=V-V=0$
So the relative separation between them $(=5km)$ always remain the same.
Now if the velocity of car (say $C$) moving in opposite direction to$A$ and $B$, is ${\overrightarrow{V}}_C$ relative to ground then the velocity of car $C$ relative to $A$ and $B$ will be ${\overrightarrow{V}}_{rel}={\overrightarrow{V}}_C-\overrightarrow{V}$
But as $\overrightarrow{V}$ is opposite to $v$
so $V_{rel}=V_c-(-30)=(V_c+30)km/hr$.
so, the time taken by it to cross the cars $A$ and $B$
$t=\frac{d}{V_{r}el}\Rightarrow \frac{4}{60}=\frac{5}{V_C+30}$
$\Rightarrow V_C=45km/hr$.