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Motion in A Plane

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Physics Part I

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Physics

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Class 10 Class 12

A river d km wide is flowing at the rate straight v subscript 1 straight m divided by straight s. A swimmer which can swim with velocity straight v subscript 2 relative to water wants to cross the river straight across. Find how long will he take to cross the river?


The path AB is the shortest path to cross the river.

To cross the river straight across along path AB, the resultant velocity of swimmer and the water flow should be along AB i.e. perpendicular to the direction of water flow.
           
To meet this condition, let the swimmer start swimming upstream at angle 0 with AB.

Therefore,

tan 90 degree space equals space fraction numerator straight v subscript 2 sin left parenthesis 90 degree plus straight theta right parenthesis over denominator straight v subscript 1 plus straight v subscript 2 cos left parenthesis 90 degree plus straight theta right parenthesis end fraction

rightwards double arrow space space space space space space space straight v subscript 1 plus straight v subscript 2 space cos left parenthesis 90 degree plus straight theta right parenthesis space equals space 0

rightwards double arrow space space space space space space space space space space space space space space space space space space space space space straight v subscript 1 minus straight v subscript 2 space sinθ space equals space 0
rightwards double arrow space space space space space space space space space space space space space space space space space space sinθ space equals space straight v subscript 1 over straight v subscript 2 

Now,
 
         straight v equals straight v subscript 2 space cosθ space equals space straight v subscript 2 square root of 1 minus sin squared straight theta end root

space space equals space straight v subscript 2 square root of 1 minus straight v subscript 1 squared over straight v subscript 2 squared end root space equals space square root of straight v subscript 2 squared minus straight v subscript 1 squared end root 

Time taken by the swimmer to cross the river is,

        space space space space space space space space space straight t equals straight d over straight v equals fraction numerator straight d over denominator square root of straight v subscript 2 squared minus straight v subscript 1 squared end root end fraction

199 Views

Give three examples of scalar quantities.

Mass, temperature and energy
769 Views

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. 


814 Views

What is a vector quantity?

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

What is a scalar quantity?

A physical quantity that requires only magnitude for its complete specification is called a scalar quantity.
1212 Views

Give three examples of vector quantities.

Force, impulse and momentum.
865 Views