Assertion (A): The magnitude of velocity of two boats relative to river is same. Both boats start simultaneously from same point on one bank. They may reach opposite bank simultaneously moving along different straight line paths.
Reason (R): For above boats to cross the river in same time, the components of their velocity relative to river in direction normal to flow should be same.
Solution:
The time to cross the river depends on the component of velocity perpendicular to the river flow (\(v_{\text{normal}}\)). For simultaneous crossing, \(v_{\text{normal}}\) must be equal for both boats. If total speed relative to river is same, and \(v_{\text{normal}}\) is same, then the magnitude of the parallel component is also same. Different paths result from different directions of the parallel component. Thus, (A) is true and (R) is true and explains (A).
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