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Physics Part I

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Two billiard balls are rolling on a flat table. One has velocity components straight v subscript straight x 1 end subscript equals 1 straight m divided by straight s semicolon space straight v subscript straight y 1 end subscript space equals space square root of 3 space straight m divided by straight s  and other has velocity components  straight v subscript straight x 2 end subscript equals 2 space straight m divided by straight s semicolon space space space straight v subscript straight y subscript 2 end subscript space equals space 2 space straight m divided by straight s. If both the balls start moving from the same point, then what is the angle between their paths?


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#6 {main}</pre> be the angles that the two balls make with X-axis.

Given, the velocity components of first ball are, 

space straight v subscript straight x 1 end subscript space equals space 1 space straight m divided by straight s 

 straight v subscript straight y 1 end subscript space equals space square root of 3 space space straight m divided by straight s

Therefore, angle is given by, 

              tanθ subscript 1 space equals space straight v subscript straight y 1 end subscript over straight v subscript straight x 1 end subscript equals fraction numerator square root of 3 over denominator 1 end fraction equals square root of 3 

rightwards double arrow               straight theta subscript 1 space equals space 60 degree

The velocity components of second ball are,

 straight v subscript straight x 2 end subscript space equals space 2 space straight m divided by straight s,

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#6 {main}</pre>

∴ angle is given by,  

                   tanθ subscript 2 equals straight v subscript straight y 2 end subscript over straight v subscript straight x 2 end subscript equals 2 over 2 equals 1

                       straight theta subscript 2 space equals space 45 degree

The angle between the paths of two ball is equal to the angle between their velocity vectors.

∴  The angle between the paths of two balls is,

                  straight theta subscript 1 minus straight theta subscript 2 equals 60 degree minus 45 degree space equals space 15 degree.

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