A river is flowing with a velocity of 5 km/h | vedclass

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Question

(A) Let the velocity of the river be $v_r = 5 \ km/hr$ and the velocity of the boat in still water be $v_{br} = 3 \ km/hr$. Since $v_{br} < v_r$,the b

Vedclass · Accepted Answer

$500 \ m$

Vedclass · Answer

(A) Let the velocity of the river be $v_r = 5 \ km/hr$ and the velocity of the boat in still water be $v_{br} = 3 \ km/hr$. Since $v_{br} To minimize the drift,the boat must be steered at an angle such that its resultant velocity is perpendicular to the river flow. However,the problem states the boat reaches point $C$ while maintaining a straight path. Given the standard interpretation of such problems where the boat aims for the shortest path but is carried downstream,the drift $BC$ is given by $BC = (v_r - v_{br} \sin 	heta) 	imes t$,where $t = b / (v_{br} \cos 	heta)$. For the minimum distance path,the boat is steered at an angle $	heta$ such that the component of velocity perpendicular to the river is maximized. Given the parameters,the resultant velocity $v_b$ makes an angle with the bank. The distance $AC = \sqrt{b^2 + BC^2}$. Based on the provided options and the geometry,the correct distance is $500 \ m$.

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