Boats Crossing River – Rankers Physics
Topic: Kinematics
Subtopic: Relative Motion in Two Dimension

Boats Crossing River


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.
 
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

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).

Leave a Reply

Your email address will not be published. Required fields are marked *