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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 100 m wide is running downwards at the rate of 1 km per hour and a swimmer who can swim at the rate of 3·6 km/hr wishes to reach a point just opposite. Along which direction should he strike and how long will he take to cross the river?

Given, 

Width of the river = 100 m 

Rate of flow of river = 1 km/hr

Rate of flow of swimmer = 3.6 km/hr



Let the swimmer dive at an angle straight theta as shown in figure to reach the point B directly opposite to A. 

From the fig., we have

∴     straight v subscript straight m sinθ space equals space straight v subscript straight r 

rightwards double arrow      sinθ space equals space straight v subscript straight r over straight v subscript straight m equals fraction numerator 1 over denominator 3.6 end fraction equals 0.278 

rightwards double arrow           straight theta equals 16.14 degree 

Therefore, the swimmer should dive at angle (90 + 16·14) =106·14° with the direction of flow.

Now,

Time taken to cross the river, t = fraction numerator AB over denominator straight v subscript straight m cosθ end fraction

                                              equals fraction numerator 0.1 over denominator 36 cross times 16.14 end fraction

                                              equals 0.0289 space hr
equals space 104.1 space straight s
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Give three examples of scalar quantities.

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What is a scalar quantity?

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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?

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