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JEE Main & Advanced Physics Two Dimensional Motion Question Bank Self Evaluation Test - Motion in a Plane

  • question_answer
    A particle of mass m is projected with a velocity u making an angle of \[30{}^\circ \] with the horizontal. The magnitude of\[({{V}_{h}}\times h)\] of the projectile when the particle is at its maximum height h

    A) \[\frac{\sqrt{3}}{2}\frac{{{\text{v}}^{\text{2}}}}{\text{g}}\]                

    B)        zero

    C) \[\frac{{{\text{v}}^{\text{2}}}}{\sqrt{2}\text{g}}\]                   

    D)         \[\frac{\sqrt{3}}{16}\frac{{{\text{v}}^{\text{2}}}}{\text{g}}\]

    Correct Answer: D

    Solution :

    [d] \[{{\text{V}}_{\text{h}}}\text{= V cos}\theta \] Where h is the maximum height \[{{V}_{h}}\times h=\left( v\cos \theta  \right)\left( \frac{{{v}^{2}}{{\sin }^{2}}\theta }{2g} \right)\] \[=\frac{{{v}^{3}}{{\sin }^{2}}\theta \cos \theta }{2g}=\frac{\sqrt{3}\,{{v}^{3}}}{16g}\]


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