Question

Two train 120m and 80m in length are running in opposite direction with velocities 42 km/hr and 30km/hr. In what time they will completely cross each other
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Answer 1

Answer

Total displacement , d = 120 m + 80 m

⇒ d = 200 m

Relative velocity , v = 42 km/h + 30 km/h

⇒ v = 72 km/h = 20 m/s

Time , t = ? s

We know that Speed is defined as velocity per time

$:\to \bf Velocity=\dfrac{Displacement}{Time}\\\\:\to \rm 20=\dfrac{200}{t}\\\\:\to \rm t=\dfrac{200}{20}\\\\:\to \rm t=10\ s$

So , Time = 10 s

Answer 2

velocity of train 1 = 42 km /hr

velocity of train 2 = 30 km/ hr

Both the trains are moving in opposite directions hence the relative velocity of train 1 with respect to train 2 will be,

V=velocity of train 1 - (- velocity of train 2 )

V=42+30

V=72 km / hr

Now in order to convert km/ hr into m/s we need to multiply by 5 /18

V=72 x 5/18 = 4 x 5 = 20 m/s

V=20 m/s

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distance covered by train 1 = length of train 1 =120 m

distance covered by train 2= length of train 2=80 m

total distance covered = 120 + 80 = 200 m

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we know that ,

$\bigstar \boxed{\mathtt{speed=\dfrac{distance}{time}}}$

Now substituting the given values in the above equation we get ,

$\rightarrow\mathtt{time=\dfrac{distance}{speed}}}$

$\rightarrow\mathtt{time=\dfrac{200}{20}}}$

$\rightarrow\boxed{\mathtt{time=10 sec}}}$

The two trains will completely cross each other in 10 seconds