A ball is thrown at an angle $\theta$ with the horizontal. Its horizontal range is equal to its maximum height. This is possible only when the value of $\tan \theta$ is ..........
$4$
$2$
$1$
$0.5$
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 body is projected at $t = 0$ with a velocity $10\,ms^{-1}$ at an angle of $60^o$ with the horizontal. The radius of curvature of its trajectory at $t=1\,s$ is $R.$ Neglecting air resistance and taking acceleration due to gravity $g = 10\,ms^{-2},$ the radius of $R$ is ........ $m$
A ball thrown by one player reaches the other in $2\, sec$. The maximum height attained by the ball above the point of projection will be about .......... $m$
Two projectiles $A$ and $B$ are thrown with the same speed but angles are $40^{\circ}$ and $50^{\circ}$ with the horizontal. Then
A particle is projected from ground with velocity $u$ at angle $\theta$ from horizontal. Match the following two columns.
Column $I$ | Column $II$ |
$(A)$ Average velocity between initial and final points | $(p)$ $u \sin \theta$ |
$(B)$ Change in velocity between initial and final points | $(q)$ $u \cos \theta$ |
$(C)$ Change in velocity between initial and final points | $(r)$ Zero |
$(D)$ Average velocity between initial and highest points | $(s)$ None of the above |