$A$ 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
$(i)$ they are moving in the same direction,and
$(ii)$ in the opposite directions is
- A$2.2$
- B$2.5$
- C$1.5$
- D$\frac{22}{11} = 2.0$
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Match Column-$I$ with Column-$II$ correctly.
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| Column-$I$ | Column-$II$ |
|---|---|
| $(1)$ Velocity of $A$ relative to $B$ if $A$ and $B$ are moving perpendicular to each other | $(a)$ $\vec{v}_{rm} = \vec{v}_r + \vec{v}_m$ |
| $(2)$ Velocity of rain drops relative to a man | $(b)$ $\vec{v}_{AB} = \vec{v}_A + \vec{v}_B$ |
| $(c)$ $v_{AB} = \sqrt{v_A^2 + v_B^2}$ |
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