Relative Velocity at JEE level (Physics)

Learn to find the minimum separation between two moving objects using relative velocity on perpendicular roads. Use ground frame calculus to obtain the minimum distance of seven by five kilometers.

Learn to solve river swimmer problems by selecting swim angles to cancel river flow, using velocity relative to river and still water, and compare direct opposite-point reach with shortest-time crossing.

Reach the opposite river bank fastest by aiming perpendicular to the flow, using full velocity to kill vertical displacement while river flow adds horizontal displacement.

Compare two river-swimmer strategies: P reaches B with a net 1.5 km/h toward the bank, while Q crosses fastest and walks to B at 3 km/h, yielding equal arrival times.

This lecture explains minimizing drift across a river with a rightward current, where the swimmer's speed is less than the current; minimum drift occurs when the resultant velocity is tangent.

Analyze two swimmers crossing a current river to reach a point on the opposite shore using relative velocity; decompose into vertical and horizontal components and include walking time.

Explore relative velocity with the rain umbrella concept: observe from the moving frame where rain appears angled, and learn to counter it by directing the umbrella in that velocity direction.

Explore velocity of approach and separation by projecting each object's velocity along the line joining them, using a cat and rat example to determine catch time.

Three particles at corners of an equilateral triangle chase each other at constant speed, tracing curved paths to center; apply calculus and shrinking-triangle and rod-rotation methods to find time.

Analyze a rectilinear pursuit where a cat always aims at a rat moving with constant speeds; derive the catch time using displacement, integration, and an along-the-line approach velocity.

Explore a swimmer aiming at B with constant speed relative to the river, while the current drifts him, to compute his drift from B to the opposite bank.