Which of the following is the graph between the height $(h)$ of a projectile and time $(t)$, when it is projected from the ground
Galileo writes that for angles of projection of a projectile at angles $(45 + \theta )$ and $(45 - \theta )$, the horizontal ranges described by the projectile are in the ratio of (if $\theta \le 45)$
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
A projectile crosses two walls of equal height $H$ symmetrically as shown The angle of projection of the projectile is
Two projectiles are thrown with same initial velocity making an angle of $45^{\circ}$ and $30^{\circ}$ with the horizontal respectively. The ratio of their respective ranges will be.
A stone is projected from the ground with velocity $25\,m/s$. Two seconds later, it just clears a wall $5 \,m$ high. The angle of projection of the stone is ........ $^o$ $(g = 10m/{\sec ^2})$