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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

A stream of width d is flowing with velocity v. A person who can swim with speed V relative to water wishes to row straight across it. In what direction should he strike out and how long would it take him to cross the stream?


To row straight across the stream, the person must strike out at angle θ upstream, such that the resultant R of his own velocity and velocity of stream is perpendicular to velocity of stream.

∴     tanθ equals fraction numerator straight V space sin left parenthesis 90 degree plus straight theta right parenthesis over denominator straight v plus Vcos left parenthesis 90 degree plus straight theta right parenthesis end fraction

        straight v plus straight V space cos left parenthesis 90 degree plus straight theta right parenthesis space equals 0

                    straight v minus Vsinθ space equals space 0

                            sinθ equals straight v over straight V

∴                         cosθ equals square root of fraction numerator straight V squared minus straight v squared over denominator straight V end fraction end root 

The swimmer should dive at an angle straight theta equals sin to the power of negative 1 end exponent left parenthesis straight v divided by straight V right parenthesis with normal to river and upstream. 

Now the resultant velocity of swimmer and the stream is, 

                Error converting from MathML to accessible text.

                Error converting from MathML to accessible text.

rightwards double arrow            Error converting from MathML to accessible text.

Therefore the time taken by swimmer to cross the river is,

                 Error converting from MathML to accessible text.

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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. 


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

Give three examples of scalar quantities.

Mass, temperature and energy
769 Views