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JEE Main & Advanced Physics Two Dimensional Motion Question Bank Mock Test - Motion in Two Dimension

  • question_answer
    Two balls A and B are thrown with speeds \[u\] and u/2, respectively. Both the balls cover the same horizontal distance before returning to the plane of projection. If the angle of projection of ball B is \[15{}^\circ \] with the horizontal, then the angle of projection of A is

    A) \[{{\sin }^{-1}}\left( \frac{1}{8} \right)\]

    B) \[\frac{1}{2}{{\sin }^{-1}}\left( \frac{1}{8} \right)\]

    C) \[\frac{1}{3}{{\sin }^{-1}}\left( \frac{1}{8} \right)\]

    D) \[\frac{1}{4}{{\sin }^{-1}}\left( \frac{1}{8} \right)\]

    Correct Answer: B

    Solution :

    [b] \[\frac{{{u}^{2}}\sin 2\theta }{g}=\frac{{{(u/2)}^{2}}\sin 30{}^\circ }{g}=\frac{{{u}^{2}}}{8g}\] \[\therefore \sin 2\theta =\frac{1}{2}\]or \[\theta =\frac{1}{2}{{\sin }^{-1}}\left( \frac{1}{8} \right)\]


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