Two trains are moving with equal speed in opp | vedclass

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(A) Let the speed of each train be $v$.Since the trains are moving in opposite directions,let the velocity of the first train be $\vec{v}_1 = v \hat{i

Vedclass · Accepted Answer

$3u$

Vedclass · Answer

(A) Let the speed of each train be $v$.Since the trains are moving in opposite directions,let the velocity of the first train be $\vec{v}_1 = v \hat{i}$ and the second train be $\vec{v}_2 = -v \hat{i}$.The wind is blowing with speed $u$ along the track,so its velocity is $\vec{v}_w = u \hat{i}$.The relative velocity of the first train with respect to the wind is $\vec{v}_{1w} = \vec{v}_1 - \vec{v}_w = (v - u) \hat{i}$.The relative velocity of the second train with respect to the wind is $\vec{v}_{2w} = \vec{v}_2 - \vec{v}_w = (-v - u) \hat{i} = -(v + u) \hat{i}$.The ratio of the magnitudes of these relative velocities is given as $1:2$.Therefore,$\frac{|v - u|}{|-(v + u)|} = \frac{1}{2}$.Assuming $v > u$,we have $\frac{v - u}{v + u} = \frac{1}{2}$.Cross-multiplying gives $2(v - u) = v + u$,which simplifies to $2v - 2u = v + u$.Solving for $v$,we get $v = 3u$.

Two trains are moving with equal speed in opposite directions along two parallel railway tracks. If the wind is blowing with speed $u$ along the track so that the relative velocities of the trains with respect to the wind are in the ratio of $1:2$,then the speed of each train must be

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