• # 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) ${{\sin }^{-1}}\left( \frac{v}{u} \right)$

[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 $AD=u\cos \theta$ $\therefore \,\,\,u\,\,\cos \theta -v=0$ $u\cos \theta =v\,\,or\,\,\theta ={{\cos }^{-1}}\left( \frac{v}{u} \right)$