trains

[vekash]

please help me for this ....


2 trains of equal length take 5 and 6s respectively to cross a pole . if these trains are moving in same direction how long will they take to cross each other?????????

 

[JeffM]

please help me for this ....


2 trains of equal length take 5 and 6s respectively to cross a pole . if these trains are moving in same direction how long will they take to cross each other?????????

Please provide the problem EXACTLY as given and tell us what you have thought about or tried in solving the problem.

 

[vekash]

in my book problem is given and its showing the answer as-
2T1*T2/T1-T2.....so the ans. is 60 sec.
its a short tech but i cant understood this.

 

[HallsofIvy]

I am going to assume that you mean that the two trains will cross a specific point in 5 s and 6 s. If we call the length of the two trains "L" meters, then the speeds of the two trains is L/5 and L/6. So the faster train is gaining on the slower with a relative speed of L/5- L/6= L/30 meters per second. I will further assume that the two trains will "cross each other" in the time it takes the faster train to go from a point where its locomotive is just meeting the end of the train to the point where the end of the faster train passes the locomotive of the slower train. Do you see that means that the faster train will have to have gone 2L at a speed of L/30 meters per second?

 

[Deleted member 4993]

in my book problem is given and its showing the answer as-
2T1*T2/(T1-T2).....so the ans. is 60 sec.
its a short tech but i cant understood this.

Please use parentheses - as shown - to indicate order of operation.

This is a problem using the equation distance = speed* time

If the length of each of the car is L

The speed of the first train V₁ = L/T1

The speed of the second train V₂ = L/T2

When these are passing each other, the relative velocity of the second train (faster) wrt the first train =

V_2/1 = V₂ - V₁ = L/T2 - L/T1 = L*(T1 - T2)/(T1*T2)

Now continue...

 

[JeffM]

in my book problem is given and its showing the answer as-
2T1*T2/T1-T2.....so the ans. is 60 sec.
its a short tech but i cant understood this.

Subhotosh Khan has shown you the quick way to solve this problem. Perhaps you will find this much longer way easier to understand. They arrive at the same result.


NAME YOUR VARIABLES

Let u = the length of both trains.

Let v = the rate of speed for the faster train.

Let w = the rate of speed for the slower train.

Let t = the time it takes the faster train to pass the slower.

Let x = the distance traveled by the slower train while being passed by the faster.

Let y = the distance traveled by the faster train while passing the slower.

NOW EXPRESS RELATIONSHIPS AMONG THE VARIABLES MATHEMATICALLY AND ELIMINATE VARIABLES

What is v in terms of u?

What is w in terms of u?

What is t in terms of x and w? So what is t in terms of x and u?

What is y in terms of x and u?

What is t in terms of y and v? So what is t in terms of x and u?

Oh my goodness. You have t in terms of x and u in two different ways, which means that you can solve for x in terms of u.

What do you get?

How does that help you?