Question

A train 100 m long is moving with a velocity of 72 km /h .Find the time it takes to cross a bridge which is 1 km long​

Answer 1

Given :

• Length of the train = 100 m

• Velocity = 72km/hr

• Length of Bridge = 1 km

To Find :

• The time taken by the train to cross the bridge

Solution :

The length of train is in metres

$\sf \: Speed = 72kmh ^{ - 1}$

$\longrightarrow \sf \: 72 \times \dfrac{5}{18}$

$\longrightarrow \sf \cancel \dfrac{360}{18} = 20ms ^{ - 1}$

To cross the bridge,the train will have to cover

[ 1 km = 1000 m ]

$\sf \: Total \: Distance = Length \: of( Bridge + Train )$

$\longrightarrow \sf \: 1000 + 100 \: m$

$\longrightarrow \sf \: 1100 \: m$

Now,We know that :

$\bigstar \: \boxed{ \sf \: Time = \dfrac{Distance }{Speed} }$

$\longrightarrow \sf \cancel\dfrac{1100}{20}$

$\longrightarrow \sf 55 \: seconds$

Hence,The time taken by the train to cross the bridge is 55 seconds.

Answer 2

SoluTion:-

Given :-

• Length of train = 100 m
• Speed of train = 72 km/h
• Length of bridge = 1 km.

To find :-

• Time taken to cross the bridge = ?

Solution 1 :-

Here,total distance to cross the bridge

↠ Total distance = Length of train + length of bridge.

↠ Total distance = 100 m + 1 km

↠ Total distance = 100/1000 km + 1 km

↠ Total distance = 0.1 km + 1 km

↠ Total distance = 1.1 km

Now given speed as 72 km/h

We know,

$\star\:\large{\boxed{\rm{\red{Time = \dfrac{Distance}{Speed} }}}}$

$\nrightarrow\sf Time \: taken = \dfrac{1.1 \: km}{72 \: km/h }\\\\\nrightarrow\large{\underline{\boxed{\sf\blue{ Time \: taken = 0.015 \: h \: \: \: [Approx.] }}}}$

$\therefore\underline{\textsf{Time \: taken = {\textbf{0.015 \: h }}}}$

$\rule{200}{2}$

Solution 2 :-

Here,total distance to cross the bridge:-

↠ Total distance = 100 m + 1 km

↠ Total distance = 100 m + 1 × 1000 m

↠ Total distance = 1100 m

Speed as given:- 72 km/h

↠ Speed = (72 × 1000) m /(60 × 60) s

↠ Speed = 72000/3600 m/s

↠ Speed of train = 20 m/s

Now using same formula i.e. Time = Distance/Speed:-

➩ Time taken = 1100 m /20 m/s

➩ Time taken = 55 s

$\therefore\underline{\textsf{Time \: taken \: to \: cross \: bridge = {\textbf{55 \: s }}}}$

Therefore,

Time taken by the train to cross the bridge is 0.015 hours or 55 seconds.