NEET Sample Paper NEET Sample Test Paper-19

  • question_answer The point from where a ball is projected is taken as the origin of the coordinate axes. The\[x\]and y components of its displacement are given by\[x=6t\]and \[y=8t-5{{t}^{2}}.\]What is the velocity of projection?

    A) \[~6\text{ }m{{s}^{-1}}\]             

    B) \[~8\text{ }m{{s}^{-1}}\]

    C) \[10\text{ }m{{s}^{-1}}\]                

    D) \[~14\text{ }m{{s}^{-1}}\]

    Correct Answer: C

    Solution :

    \[X=6t\]and \[y=8t-5{{t}^{2}}\] \[\frac{dx}{dt}={{v}_{x}}=6\] \[\frac{dv}{dt}={{v}_{y}}=8-10t,\]\[\therefore \]\[{{\left. \frac{dy}{dt} \right|}_{t=0}}=8\] \[\therefore \]\[v=\sqrt{{{v}_{x}}+v_{y}^{2}}=\sqrt{{{6}^{2}}+{{8}^{2}}}=10\,m/s\] Hence, the correction option is [c].


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