Two cars are moving in the same direction wit | vedclass

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Question

(b) The two car (say $A$ and $B$) are moving with same velocity, the relative velocity of one (say $B$) with respect to the other $A,\,{\overrightarro

Vedclass · Accepted Answer

$45$

Vedclass · Answer

(b) The two car (say $A$ and $B$) are moving with same velocity, the relative velocity of one (say $B$) with respect to the other $A,\,{\overrightarrow v _{BA}} = {\overrightarrow v _B} - {\overrightarrow v _A} = v - v = 0$

So the relative separation between them ($= 5\, km$) always remains the same.

Now if the velocity of car (say $C$) moving in opposite direction to $A$ and $B$, is ${\overrightarrow v _C}$ relative to ground then the velocity of car $C$ relative to $A$ and $B$ will be

${\overrightarrow v _{rel.}} = {\overrightarrow v _C} - \overrightarrow v $

But as $\overrightarrow v $ is opposite to $v_C$

So $\,{v_{rel}} = {v_C} - ( - 30) = ({v_C} + 30)\,km/hr.$

So, the time taken by it to cross the cars $A$ and $B$

$t = \frac{d}{{{v_{rel}}}}\,\,\,\, \Rightarrow \,\,\,\frac{4}{{60}} = \frac{5}{{{v_C} + 30}}\,\,$

$ \Rightarrow \,\,\,{v_C} = 45\,km/hr.$

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