A projectile is projected with velocity of $25\, m / s$ at an angle $\theta$ with the horizontal. After t seconds its inclination with horizontal becomes zero. If $R$ represents horizontal range of the projectile, the value of $\theta$ will be : [use $g =10 m / s ^{2}$ ]

  • [JEE MAIN 2022]
  • A

    $\frac{1}{2} \sin ^{-1}\left(\frac{5 t^{2}}{4 R}\right)$

  • B

    $\frac{1}{2} \sin ^{-1}\left(\frac{4 R }{5 t ^{2}}\right)$

  • C

    $\tan ^{-1}\left(\frac{4 t ^{2}}{5 R }\right)$

  • D

    $\cot ^{-1}\left(\frac{ R }{20 t ^{2}}\right)$

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A particle of mass $100\,g$ is projected at time $t =0$ with a speed $20\,ms ^{-1}$ at an angle $45^{\circ}$ to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time $t=2\,s$ is found to be $\sqrt{ K }\,kg\,m ^2 / s$. The value of $K$ is $............$ $\left(\right.$ Take $\left.g =10\,ms ^{-2}\right)$

  • [JEE MAIN 2023]

Two particles are projected from the same point with the same speed $u$ such that they have the same range $R$, but different maximum heights, $h_1$ and $h_2$. Which of the following is correct ?

  • [JEE MAIN 2019]

A stone is thrown at an angle $\theta $ to the horizontal reaches a maximum height $H$. Then the time of flight of stone will be

Match the columns

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