Assertion : The magnitude of velocity of two | vedclass

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Question

(A) The time taken to cross a river of width $d$ is given by $t = \frac{d}{v_y}$,where $v_y$ is the component of the boat's velocity relative to the r

Vedclass · Accepted Answer

If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.

Vedclass · Answer

(A) The time taken to cross a river of width $d$ is given by $t = \frac{d}{v_y}$,where $v_y$ is the component of the boat's velocity relative to the river in the direction normal to the river flow.If the magnitudes of the velocities of two boats relative to the river are the same $(v_1 = v_2 = v)$,and they are directed at the same angle $	heta$ with respect to the normal to the river bank,then their normal components are $v_y = v \cos 	heta$.Since $v$ and $	heta$ are the same for both boats,their normal components $v_y$ are identical.Therefore,both boats will cross the river in the same time $t = \frac{d}{v \cos 	heta}$,even if they follow different paths due to the river's flow.Thus,both the Assertion and the Reason are correct,and the Reason is the correct explanation of the Assertion.

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