Question

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

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

Answer 1

The correct option is C $45km/hr$

Consider two cars $A\&B$ moving with same velocity.
Hence,
Relative velocity of $B$ with respect to the other $A$,
${\overrightarrow{v}}_{BA}={\overrightarrow{v}}_B-{\overrightarrow{v}}_A$
${\overrightarrow{v}}_{BA}=v-v=30-30$
${\overrightarrow{v}}_{BA}=0$
So, the relative separation between them $(=5km)$ always remains the same.
Now, consider the velocity of car $C$ moving in opposite direction to $A$ and $B$,
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$v_C$
So
$v_{rel}.=v_c-(-30)$
$=(v_C+30)km/hr$. ….(𝑖)
Therefore, the time taken by it to cross the cars $A$ and $B$
$t=\frac{d}{v_{rel}}$ ..(𝑖𝑖)
By putting equation (𝑖) in equation (𝑖𝑖) we get,
$t=\frac{4}{60}=\frac{5}{v_C+30}4(v_c+30)=5\times 604v_c+1200=300⟹4v_c=900v_C=45km/hr$