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Two ships and can establish mutual communication when they are not more than apart. At midnight, the ship moving towards north with a constant velocity of passes a location east of ship A, that is moving with a constant velocity of towards northeast. If time interval (in seconds) for which they remain in communication is , find .

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Important Questions on Motion in a Plane
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The time period of a particle moving along a circular path of radius is Another particle starts from rest at a point and travelling along a straight line path reaches the point in . If and the particles and are respectively at and at an instant shown in the figure, the acceleration of particle with respect to particle is _______. (Points and lie along the same straight line)

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A swimmer wants to cross a river from point to point . Line AB makes an angle of with the flow of the river. The magnitude of the velocity of the swimmer is the same as that of the river. The angle with the line should be _______, so that the swimmer reaches point .

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