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Motion in A Plane

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Physics Part I

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Physics

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CBSE Gujarat Board Haryana Board

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Class 10 Class 12
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,
             straight t subscript 1 equals fraction numerator straight d over denominator straight v minus straight u end fraction plus fraction numerator straight d over denominator straight v plus straight u end fraction equals fraction numerator 2 vd over denominator straight v squared minus straight u squared end fraction

rightwards double arrow                               space straight t subscript 1 equals fraction numerator 2 cross times 5 cross times begin display style 1 half end style over denominator 5 squared minus 3 squared end fraction

space space space equals 5 over 16 hr space

space space equals space 18 space min space 45 sec

Swimmer B:

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

                      sinθ space equals straight u over straight v equals 3 over 5



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


  straight t subscript 2 equals 2 cross times fraction numerator straight d over denominator straight v space cosθ end fraction

space space equals 2 cross times fraction numerator 1 divided by 2 over denominator 5 cross times 0.8 end fraction

space space equals 1 fourth hr

space space equals 15 min

The difference of the time taken by two swimmers is,

                increment straight t space equals space straight t subscript 1 minus straight t subscript 2 space

space space space space space space equals space 3 space min space 45 space sec. 

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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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What is a scalar quantity?

A physical quantity that requires only magnitude for its complete specification is called a scalar quantity.
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Give three examples of scalar quantities.

Mass, temperature and energy
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Give three examples of vector quantities.

Force, impulse and momentum.
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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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