Two objects are thrown up at angles of $45^{\circ}$ and $60^{\circ}$ respectively,with the horizontal. If both objects attain the same vertical height,then the ratio of the magnitude of velocities with which these are projected is .........

$A$ projectile is thrown with speed $40 \, m/s$ at an angle $\theta$ from the horizontal. It is found that the projectile is at the same height at $1 \, s$ and $3 \, s$. What is the angle of projection?

$A$ ball is projected with kinetic energy $E$ at an angle of $45^\circ$ to the horizontal. At the highest point during its flight,its kinetic energy will be

The trajectory of a projectile in a vertical plane is $y = \alpha x - \beta x^2$,where $\alpha$ and $\beta$ are constants and $x$ and $y$ are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection $\theta$ and the maximum height attained $H$ are respectively given by:

$A$ projectile is thrown into space so as to have maximum horizontal range $R$. Taking the point of projection as the origin,the coordinates of the point where the speed of the particle is minimum are:

$A$ bullet is fired with a velocity $u$ making an angle of $60^{\circ}$ with the horizontal plane. The horizontal component of the velocity of the bullet when it reaches the maximum height is