Motion in A Plane

Physics Part I

Physics

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Two men A and B can swim in still water, at the rate of 5km/hr. The man A swims upstream a distance half km equal to width of river and B swims straight across the river and back again. Assuming that the velocity of river is 3 km/hr, find the difference in the time taken by them.

Here, velocity of man is, v = 5 km/hr

Velocity of river is, u = 3 km/hr, along QP.

Swimmer A:

Velocity of swimmer A w.r.t. bank while going from P to Q = v - u

Velocity of swimmer A w.r.t. bank while coming back from Q to P = v + u

Time taken by swimmer A to make the round trip is,

Swimmer B:

To cross the river straight across man will dive at angle given by,

Therefore time taken by man B to make the round trip is,

The difference of the time taken by two swimmers is,

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What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

A quantity must possess the direction and must follow the vector axioms. Any quantity that follows the vector axioms are classified as vectors.

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What is a vector quantity?

A physical quantity that requires direction along with magnitude, for its complete specification is called a vector quantity.

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