A missile is fired for maximum range with an initial velocity of $20\; m/s$. If $g = 10 \;m/s^2$ , the range of the missile is ...... $m$
$20$
$50$
$40$
$60$
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
The maximum height attained by a projectile is increased by $10\,\%$ by increasing its speed of projection, without changing the angle of projection. The percentage increases in the horizontal range will be $...........\,\%$
Two bodies are projected from ground with same speeds $40 ms ^{-1}$ at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of $60^{\circ}$, with horizontal then sum of the maximum heights, attained by the two projectiles, is $.......m$. (Given $g =10 ms ^{-2}$ )
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 ball is thrown from the ground to clear a wall $3\,m$ high at a distance of $6\,m$ and falls $18\,m$ away from the wall, the angle of projection of ball is