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J & K CET Engineering J and K - CET Engineering Solved Paper-2010

  • question_answer
    Let \[\vec{u}\] and \[\vec{v}\] be the velocity vectors of a particle at a point O. If \[\vec{u}\] and \[\vec{v}\] are in opposite directions and if \[u>v,\] then the magnitude of the resultant velocity vector \[\vec{v}\] is

    A)  \[u+v\]          

    B)  \[2\,u+v\]

    C)  \[u-v\]

    D)  \[u-\frac{1}{2}v\]

    Correct Answer: C

    Solution :

    Since, \[\vec{u}\] and \[\vec{v}\] are in opposite directions, therefore angle between them is\[{{180}^{o}}\]. Now, magnitude of resultant velocity is \[\sqrt{{{u}^{2}}+{{v}^{2}}+2uv\,\cos \,{{180}^{o}}}\] \[=\sqrt{{{u}^{2}}+{{v}^{2}}-2uv}=u-v\]


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