A projectile has initially the same horizontal velocity as it would acquire if it had moved from rest with uniform acceleration of $3\, ms^{-2}$ for $ 0.5\, minutes$. If the maximum height reached by it is $80\, m$, then the angle of projection is (Take $g = 10\, ms^{-2}$)
${\tan ^{ - 1}}\,\left( 3 \right)$
${\tan ^{ - 1}}\,\left( {\frac{3}{2}} \right)$
${\tan ^{ - 1}}\,\left( {\frac{4}{9}} \right)$
${\sin ^{ - 1}}\,\left( {\frac{4}{9}} \right)$
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 |
A stone is just released from the window of a train moving along a horizontal straight track. The stone will hit the ground following
A projectile is thrown into space so as to have a maximum possible horizontal range of $400$ metres. Taking the point of projection as the origin, the co-ordinates of the point where the velocity of the projectile is minimum are
Two bodies are thrown up at angles of $45^o$ and $60^o$, respectively, with the horizontal. If both bodies attain same vertical height, then the ratio of velocities with which these are thrown is
A projectile has the same range $R$ for two angles of projection. If $T_1$ and $T_2$ be the times of flight in the two cases, then $R$ is