A boy playing on the roof of a $10\, m$ high building throws a ball with a speed of $10\,m/s$ at an angle of $30^o$ with the horizontal. How far from the throwing point will the ball be at the height of $10\, m$ from the ground ? $\left[ {g = 10\,m/{s^2},\sin \,{{30}^o} = \frac{1}{2},\cos \,{{30}^o} = \frac{{\sqrt 3 }}{2}} \right]$
A boy playing on the roof of a $10\, m$ high building throws a ball with a speed of $10\,m/s$ at an angle of $30^o$ with the horizontal. How far from the throwing point will the ball be at the height of $10\, m$ from the ground ? $\left[ {g = 10\,m/{s^2},\sin \,{{30}^o} = \frac{1}{2},\cos \,{{30}^o} = \frac{{\sqrt 3 }}{2}} \right]$
- A
$5\sqrt 5 $
- B
$6$
- C
$3$
- D
$5\sqrt 3 $
Similar Questions
A shell fired from the base of a mountain just clears it. If $\alpha$ is the angle of projection then the angular elevation of the summit $\beta$ is
A shell fired from the base of a mountain just clears it. If $\alpha$ is the angle of projection then the angular elevation of the summit $\beta$ is
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
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 $\theta \le 45)$
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 $\theta \le 45)$
A projectile crosses two walls of equal height $H$ symmetrically as shown The time of flight $T$ is given by ........ $\sec$
A projectile crosses two walls of equal height $H$ symmetrically as shown The time of flight $T$ is given by ........ $\sec$
Two projectiles $A$ and $B$ are thrown with initial velocities of $40\,m / s$ and $60\,m / s$ at angles $30^{\circ}$ and $60^{\circ}$ with the horizontal respectively. The ratio of their ranges respectively is $\left( g =10\,m / s ^2\right)$
Two projectiles $A$ and $B$ are thrown with initial velocities of $40\,m / s$ and $60\,m / s$ at angles $30^{\circ}$ and $60^{\circ}$ with the horizontal respectively. The ratio of their ranges respectively is $\left( g =10\,m / s ^2\right)$
- [JEE MAIN 2023]