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

Answer 1

Answer: (B)

45 km/hr

Answer 2

The two car (say A and B) are moving with same velocity, the relative velocity of one (say B) with respect to the other $A, ⥂ {\overset{\rightarrow}{v}}_{BA} = {\overset{\rightarrow}{v}}_{B} - {\overset{\rightarrow}{v}}_{A} = v - v = 0$

So the relative separation between them (= 5 km) always remains the same.

Now if the velocity of car (say C) moving in opposite direction to A and B, is ${\overset{\rightarrow}{v}}_{C}$ relative to ground then the velocity of car C relative to A and B will be ${\overset{\rightarrow}{v}}_{rel.} = {\overset{\rightarrow}{v}}_{C} - \overset{\rightarrow}{v}$

But as $\overset{\rightarrow}{v}$ is opposite to v_C so

$v_{rel} = v_{c} - ( - 30) = (v_{C} + 30)km/hr.$

So, the time taken by it to cross the cars A and B $t = \frac{d}{v_{rel}} ⥂ \Rightarrow \frac{4}{60} = \frac{5}{v_{C} + 30} \Rightarrow v_{C} = 45km/hr.$