KVPY Sample Paper KVPY Stream-SX Model Paper-5

  • question_answer
    A smooth square platform ABCD is moving towards right with a uniform speed \[v.\] At what angle \[\theta \] must a particle be projected from A with speed \[u\]so that it strikes the point B ?

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

    B) \[{{\cos }^{-1}}\left( \frac{v}{u} \right)\]

    C) \[{{\cos }^{-1}}\left( \frac{u}{v} \right)\]                       

    D) \[{{\sin }^{-1}}\left( \frac{v}{u} \right)\]

    Correct Answer: B

    Solution :

    [B] Particle will strike the point B is velocity of particle with respect to platform is along AB or component of its relative velocity along AD is zero. i.e., Velocity of particle projected from A along \[AD=u\cos \theta \] \[\therefore \,\,\,u\,\,\cos \theta -v=0\] \[u\cos \theta =v\,\,or\,\,\theta ={{\cos }^{-1}}\left( \frac{v}{u} \right)\]

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