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  • I have a doubt, kindly clarify. A passenger train of length 60 m travels at a speed of 80 km/hr. Another freight train of length 120 m travels at a speed of 30 km/hr. The ratio of times taken by the passenger train to completely cross the freight train wh

A passenger train of length 60 m travels at a speed of 80 km/hr. Another freight train of length 120 m travels at a speed of 30 km/hr. The ratio of times taken by the passenger train to completely cross the freight train when : (i) they are moving in the same direction , and (ii) in the opposite directions is : 

  • Option 1)

    \frac{5}{2}

  • Option 2)

    \frac{3}{2}

  • Option 3)

    \frac{11}{5}

  • Option 4)

    \frac{25}{11}

Answers (1)

best_answer

 

Case of Relative velocity. -

When A and B are moving along a straight line in the same direction.

\underset{V_A}{\rightarrow} = Velocity of object A.

\underset{V_B}{\rightarrow} = Velocity of object B.

Relative velocity  of A wr to B is

\vec{V}_{AB}=\vec{V}_{A}-\vec{V}_{B}

\vec{V}_{AB},\vec{V}_{A},\vec{V}_{B} All are in same direction.(If \vec{V}_{A}> \vec{V}_{B})

and Relative velocity  of B wr to A is

\vec{V}_{BA}=\vec{V}_{B}-\vec{V}_{A}

&  \vec{V}_{AB}=-\vec{V}_{BA}

 

 

- wherein

a)   \vec{V}_{AB}=\vec{V}_{A}-\vec{V}_{B}

        = (20 - 5) ms-1

        = 15 ms-1

b)    \vec{V}_{BA}=\vec{V}_{B}-\vec{V}_{A}

         = (5 - 20) ms-1

         = - 15 ms-1

 

A                                                             B

l=60m \, \, \, \, \, \, \, \, \, \, \, \, \, \, \,\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, l=120m

V_{A}=80km/hr \, \, \, \, \, \, \, \, \, \, \, V_{B}=30km/hr

\left ( 1 \right )\underset{V_{A}}{\rightarrow}\, \, \underset{V_{B}}{\leftarrow}\, \, \, \, \, \, \, t_{1}=\frac{x}{V_{A}-V_{B}}=\frac{X}{50}\, \, \, \, \, \left ( 3 \right )

                           let    X= total train length of both train A&B

\left ( 2 \right ) \underset{V_{A}}{\leftarrow}\, \, \underset{V_{B}}{\rightarrow}\, \, \, \, \, \, \, t_{2}=\frac{x}{V+U}=\frac{X}{100}\, \, \, \, \, \left ( 4 \right )

 

from (3) & (4)

\frac{t_{1}}{t_{2}}=\frac{11}{5}

 

 

 


Option 1)

\frac{5}{2}

Option 2)

\frac{3}{2}

Option 3)

\frac{11}{5}

Option 4)

\frac{25}{11}

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