Velocity of train if it passes 2km bridge in 110sec and a point in 10s

[Govind_Balaji]

Homework Statement

A train passes through an electric post in 10 seconds. With same velocity, it passes through a 2km long bridge in 110 seconds.Find the velocity of the train:

a)18kmph b)36kmph c)72kmph d)90kmph.

Homework Equations

The Attempt at a Solution

The train passes through the electric post in 10s. Let it velocity be $v$.

$\Rightarrow \text{Length of the train} = 10v$

Then I calculated the change in displacement of the train with respect to the bridge when it passes through.

https://www.physicsforums.com/attachment.php?attachmentid=70093&stc=1&d=1401201462

$\text{Displacement of train from bridge after overtake}=2km+10v$
$\text{Displacement of train from bridge after overtake}=-2km$

$\delta s=(2km+10v)-(-2km)=4km+10v$

It took 110 seconds for the train.
Its displacement=$110v$

$\Rightarrow Displacement=110v=4km+10v$

$v=\frac{4*3600}{100}km/h \Rightarrow v=108km/h$

But itsn't in the options.

 

[NascentOxygen]

The train passes through the electric post in 10s. Let it velocity be $v$.

$\Rightarrow \text{Length of the train} = 10v$ ✔

Then I calculated the change in displacement of the train with respect to the bridge when it passes through.

$\text{Displacement of train from bridge after overtake}=2km+10v$ ✔

The train covers this 2000 + 10v distance in 110 secs, so speed v = ...

 

[adjacent]

Whah? How did you draw that tick? $\text{Nascent}O_2$?

 

[Govind_Balaji]

The train covers this 2000 + 10v distance in 110 secs, so speed v = ...

If i take it 2km+10v, then I get 72km/h.

But why should I take 2km+10v instead of 4km+10v?

Isn't 110 seconds is the time from when the train's engine entered the bridge till the train completely left the bridge?

Or is 110 seconds is the time from when the train's engine entered the bridge till the train's engine left the bridge?

Also, how did you place that tick??

 

[mafagafo]

Whah? How did you draw that tick? $\text{Nascent}O_2$?

color="seagreen"
size="7"
✔
/size
/color

Just use the brackets. Result:
✔

I do not know if there is another way.

 

[NascentOxygen]

If i take it 2km+10v, then I get 72km/h.

But why should I take 2km+10v instead of 4km+10v?

Draw a diagram showing the last carriage exiting the bridge. Where is the engine at this juncture?

 

[SammyS]

Isn't 110 seconds is the time from when the train's engine entered the bridge till the train completely left the bridge?

It's clear from the figure, that the above interpretation is the correct one.

(There's also a quite simple way to do this problem, but I suspect that you're expected to do it with Algebra.)

Or is 110 seconds is the time from when the train's engine entered the bridge till the train's engine left the bridge?

 

[Govind_Balaji]

Draw a diagram showing the last carriage exiting the bridge. Where is the engine at this juncture?

I made a small mistake. I calculated displacement in first diagram w.r.t. the start of the bridge.

But I calculated the displacement in second diagram w.r.t the end of the bridge.

Thanks for all of your help.

 

[SammyS]

I made a small mistake. I calculated displacement in first diagram w.r.t. the start of the bridge.

But I calculated the displacement in second diagram w.r.t the end of the bridge.

Thanks for all of your help.

As a check:

From the time the locomotive (assumed at the front of the train) gets to the end of bridge, to the time the last train car just clears the end of the bridge, 10 seconds elapse.

So it took the locomotive 100 seconds to cross the bridge.

That's 2km in 100 seconds.