If $R$ and $H$ are the horizontal range and maximum height attained by a projectile, than its speed of projection is ..........

  • A

    $\sqrt{2 g R+\frac{4 R^2}{g H}}$

  • B

    $\sqrt{2 g H+\frac{R^2 g}{8 H}}$

  • C

    $\sqrt{2 g H+\frac{8 H}{R g}}$

  • D

    $\sqrt{2 g H+\frac{R^2}{H}}$

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A particle is thrown with a velocity of $u \,m / s$. It passes $A$ and $B$ as shown in figure at time $t_1=1 \,s$ and $t_2=3 \,s$. The value of $u$ is ....... $m / s$ $\left(g=10 \,m / s ^2\right)$

Match the columns

  Column $-I$
    $R/H_{max}$
  Column $-II$
  Angle of projection $\theta $
   $A.$ $1$    $1.$ ${60^o}$
   $B.$ $4$    $2.$ ${30^o}$
   $C.$ $4\sqrt 3$    $3.$ ${45^o}$
   $D.$ $\frac {4}{\sqrt 3}$    $4.$ $tan^{-1}\,4\,=\,{76^o}$