Answers

2014-05-18T12:47:03+05:30
Here, I shall introduce somewhat of relative velocity, because this is answer zone, and i would like to introduce some shortcut methods, but still, please refer to some other books and theories and ask teachers for the correct methodology of solving the question.
Relative speed is equal to  \sqrt{ a^{2} +  b^{2} - 2ab*Cos \alpha  }
Here,  \alpha [called Alpha] represents the angle between the direction of velocities of the two objects in motion. 
So, if the two objects are moving in opposite direction, like   <-- -->  or --> <-- so, the angle is 180 degrees and the equation will be  \sqrt{ a^{2} + b^{2} - 2ab*Cos \ 180 } and since Cos 180 is -1, the equation will be reduced to  \sqrt{ a^{2} +  b^{2} +2ab  } and the Relative or NET Speed will be a+b similarly, if both are moving are in same direction,i.e either ---> ----> or <---<--- the angle of direction will be zero, and we can write the Relative or NET speed as a-b [Cos 0 = 1]. 

In the question:-

Lets first convert kmph into SI Unit system, that is, in mps.
So, 81 kmph = 81 * 5/18 = 22.5 mps 
and 72 kmph = 72 * 5/18 = 20 mps [now do not ask how we get 5/18 :D, it is 1000/3600] 
The question also tells that both trains are moving in opposite direction and cross each other COMPLETELY, please keep in mind it is COMPLETELY in some given time. 
So, just think if the train has to cross a station, it will first enter the station from the engine, and the engine has to move through the whole station length, and thus the train too. The train then has to move out COMPLETELY from the station's length. So, the total distance covered while crossing the station will be length of station +
 the length of train.
Similarly, in this question, since the train has to cross the other train, it needs to cover the length of the other train as well as of its own. Let the length of the other train be x meters.

NOW :-
Relative speed will be a + b = 22.5 + 20 =42.5 mps
Total distance will be length of two trains added up = 210 + x
Time is given as 16 seconds.
Now Time = Distance/Speed 
so, 16 = ( 210 + x )/42.5 
after solving, we get 210 + x = 680
=> x = 680 - 210 = 470 meters. 
So, the length of the other train will be 470 meters. 
Good if understood, if not, please comment below, I will follow it up :-) 

3 3 3
2014-05-18T13:07:54+05:30
Relative velocity of both train = 72 -(-81)
                                        = 153 Km/hr
                                        = 153*5/18  m/sec.
                                         = 85/2  m/sec.
let length of train B is x
total distance travel by both train = 210 + x
210+x = 85*16/2
x = 680-210
x = 470m.

1 1 1