The velocity at the maximum height of a projectile is $\frac{\sqrt{3}}{2}$ times its initial velocity of projection $(u)$. Its range on the horizontal plane is .............

  • A

    $\frac{\sqrt{3} u^2}{2 g}$

  • B

    $\frac{3 u^2}{2 g}$

  • C

    $\frac{3 u^2}{g}$

  • D

    $\frac{u^2}{2 g}$

Similar Questions

A body is thrown at angle $30^{\circ}$ to the horizontal with the velocity of $30\; m / s$. After $1\;sec$, its velocity will be (in $m/s$) $\left(g=10\; m / s ^{2}\right)$

A projectile is thrown with an initial velocity of $(a \hat{ i }+b \hat{ j }) ms ^{-1}$. If the range of the projectile is twice the maximum height reached by it, then

      Column $-I$

    Angle of projection

    Column $-II$
  $A.$ $\theta \, = \,{45^o}$   $1.$ $\frac{{{K_h}}}{{{K_i}}} = \frac{1}{4}$
  $B.$ $\theta \, = \,{60^o}$   $2.$ $\frac{{g{T^2}}}{R} = 8$
  $C.$ $\theta \, = \,{30^o}$   $3.$ $\frac{R}{H} = 4\sqrt 3 $
  $D.$ $\theta \, = \,{\tan ^{ - 1}}\,4$   $4.$ $\frac{R}{H} = 4$

$K_i :$ initial kinetic energy

$K_h :$ kinetic energy at the highest point

If a body $A$ of mass $M$ is thrown with velocity $v$ at an angle of ${30^o}$ to the horizontal and another body $B$ of the same mass is thrown with the same speed at an angle of ${60^o}$ to the horizontal. The ratio of horizontal range of $A$ to $B$ will be

  • [AIPMT 1992]

From the top of a tower of height $40\,m$, a ball is projected upwards with a speed of $20\,m / s$ at an angle of elevation of $30^{\circ}$. The ratio of the total time taken by the ball to hit the ground to its time of flight (time taken to come back to the same elevation) is (take $g=10\,m / s ^2$ )