$A$ bomb of mass $m$ is projected from the ground with speed $v$ at an angle $\theta$ with the horizontal. At the maximum height from the ground,it explodes into two fragments of equal mass. If one fragment comes to rest immediately after the explosion,then the horizontal range of the centre of mass is ..............
- A$\frac{v^2 \sin^2 \theta}{g}$
- B$\frac{v^2 \sin \theta}{g}$
- C$\frac{v^2 \sin \theta}{2g}$
- D$\frac{v^2 \sin 2\theta}{g}$
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It is possible to project a particle with a given velocity in two possible ways so as to make them pass through a point $P$ at a horizontal distance $r$ from the point of projection. If $t_1$ and $t_2$ are times taken to reach this point in two possible ways,then the product $t_1 t_2$ is proportional to
DifficultTS EAMCET 2012
View Solution$A$ projectile is launched from the ground, such that it hits a target on the ground which is $90 \,m$ away. The minimum velocity of the projectile to hit the target is (acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,ms^{-1}$)
The equation of motion of a projectile is $y = ax - bx^2$,where $a$ and $b$ are constants. Match the Column-$I$ with Column-$II$:
Column-$I$ Column-$II$ $i)$ The initial velocity of projection $a)$ $\sqrt{\frac{g(1+a^2)}{2b}}$ $ii)$ The horizontal range of projectile $b)$ $\frac{a}{b}$ $iii)$ The maximum height attained by projectile $c)$ $\frac{a^2}{4b}$ $iv)$ The time of flight of projectile $d)$ $a\sqrt{\frac{2}{bg}}$
| Column-$I$ | Column-$II$ |
| $i)$ The initial velocity of projection | $a)$ $\sqrt{\frac{g(1+a^2)}{2b}}$ |
| $ii)$ The horizontal range of projectile | $b)$ $\frac{a}{b}$ |
| $iii)$ The maximum height attained by projectile | $c)$ $\frac{a^2}{4b}$ |
| $iv)$ The time of flight of projectile | $d)$ $a\sqrt{\frac{2}{bg}}$ |
If the time of flight of a bullet over a horizontal range $R$ is $T \ s$,the inclination of the direction of projection to the horizontal is
Medium
View SolutionAt what angle of elevation should a projectile be projected with a velocity of $20 \, m/s$ to reach a maximum height of $10 \, m$ (in $^{\circ}$)?
Easy
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