A bullet is fired from a cannon with velocity $500 \,m/s$. If the angle of projection is ${15^o}$ and $g = 10m/{s^2}$. Then the range is
A bullet is fired from a cannon with velocity $500 \,m/s$. If the angle of projection is ${15^o}$ and $g = 10m/{s^2}$. Then the range is
- A
$25 \times {10^3}m$
- B
$12.5 \times {10^3}m$
- C
$50 \times {10^2}m$
- D
$25 \times {10^2}m$
Similar Questions
A particle is projected from the ground with velocity $u$ at angle $\theta$ with horizontal. The horizontal range, maximum height and time of flight are $R, H$ and $T$ respectively. They are given by $R = \frac{{{u^2}\sin 2\theta }}{g}$, $H = \frac{{{u^2}{{\sin }^2}\theta }}{{2g}}$ and $T = \frac{{2u\sin \theta }}{g}$ Now keeping $u $ as fixed, $\theta$ is varied from $30^o$ to $60^o$. Then,
A particle is projected from the ground with velocity $u$ at angle $\theta$ with horizontal. The horizontal range, maximum height and time of flight are $R, H$ and $T$ respectively. They are given by $R = \frac{{{u^2}\sin 2\theta }}{g}$, $H = \frac{{{u^2}{{\sin }^2}\theta }}{{2g}}$ and $T = \frac{{2u\sin \theta }}{g}$ Now keeping $u $ as fixed, $\theta$ is varied from $30^o$ to $60^o$. Then,
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
|
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 particle is projected from ground with speed $80 \,m / s$ at angle $30^{\circ}$ with horizontal from ground. The magnitude of average velocity of particle in time interval $t=2 \,s$ to $t=6 \,s$ is ....... $m / s$ [Take $g=10 \,m / s ^2$ ]
A particle is projected from ground with speed $80 \,m / s$ at angle $30^{\circ}$ with horizontal from ground. The magnitude of average velocity of particle in time interval $t=2 \,s$ to $t=6 \,s$ is ....... $m / s$ [Take $g=10 \,m / s ^2$ ]
A particle of mass $100\,g$ is projected at time $t =0$ with a speed $20\,ms ^{-1}$ at an angle $45^{\circ}$ to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time $t=2\,s$ is found to be $\sqrt{ K }\,kg\,m ^2 / s$. The value of $K$ is $............$ $\left(\right.$ Take $\left.g =10\,ms ^{-2}\right)$
A particle of mass $100\,g$ is projected at time $t =0$ with a speed $20\,ms ^{-1}$ at an angle $45^{\circ}$ to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time $t=2\,s$ is found to be $\sqrt{ K }\,kg\,m ^2 / s$. The value of $K$ is $............$ $\left(\right.$ Take $\left.g =10\,ms ^{-2}\right)$
- [JEE MAIN 2023]
A projectile is thrown with velocity $u$ making angle $\theta$ with vertical. It just crosses the tops of two poles each of height $h$ after $1\,s$ and $3\,s$, respectively. The maximum height of projectile is ............ $m$
A projectile is thrown with velocity $u$ making angle $\theta$ with vertical. It just crosses the tops of two poles each of height $h$ after $1\,s$ and $3\,s$, respectively. The maximum height of projectile is ............ $m$