There is A one-way road one km long with two lanes, each lane five meters broad. Cars Cruise at 60 kmph on each lane. Distance between front bumpers of any two Successive cars is 10 meters which includes length of one car plus the clear Between the two cars. question (a): how many cars exit the road in one hour (your brilliant readers will find this childs play). then one morning mtnl digs a trench across one Lane at location half km of road length. The trench is 5m x 5m which makes a Single lane road for 10 meters (2.5 meters on either side of the trench for Maneuvering). As the driving discipline and etiquette of indian rivers is World famous they allow five cars from one lane and then five cars from The other lane to enter the single lane portion of the road. This Involves deceleration, stoppage and acceleration of cars. Assume optimum Points of stoppage and from the cruising speed. Question (b): how many cars Exit the road in one hour?

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shashank_tangwan

  • Mar 31st, 2007
 

 It' surprising that no one tried this Qn. for such long.... anyways , here's what I think of it :

(a)  Since the velocity of the car is given as 60 kmph or 50/3 metres /sec ,  hence it passes 50/3 metres of the road in one second. Now given that cars are spaced 10metres apart & a car travels at the given speed , it follows that in one second 5/3 cars pass across any part of the lane. which means that in 1 hr,  (5/3) * 3600 or 6000 cars exit a single lane of the road. 

Thus in all , 12000 cars exit the road in 1 hr..

(b) Now  when the trench is dug and only one lane of the road is operational , it creates a bottleneck accross that stretch of the road and one can say that for that stretch , only one lane is operational.....

so consider that all the cars exiting the road have to pass thru that bottleneck  which means that the No. of cars exiting the road is equal to the No. of cars exiting  the bottleneck. 

If we take the optimal conditions of breaking & accelerating etc. and also that there is sufficient space for the cars to maneuvere the trench, we again find that the No. of cars exiting the bottleneck in an hour is 6000 as found in part  (a)..

Hence the No. of cars exiting the road per hour after the trench is dug is  6000

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