Two projectiles thrown at $30^{\circ}$ and $45^{\circ}$ with the horizontal respectively,reach the maximum height in the same time. The ratio of their initial velocities is

$A$ bomb is dropped by an airplane flying horizontally with a velocity of $200 \text{ km/hr}$ at a height of $980 \text{ m}$. At the time of dropping the bomb,the horizontal distance of the airplane from the target on the ground to hit it directly is (given $g = 9.8 \text{ m/s}^2$):

$A$ stone is projected at an angle $\theta$ with velocity $u$. If it executes nearly a circular motion at its maximum point for a short time,the radius of the circular path will be ($g=$ acceleration due to gravity).

$A$ projectile is thrown with an initial velocity $(a \hat{i} + b \hat{j}) \ m/s$,where $\hat{i}$ and $\hat{j}$ are unit vectors along horizontal and vertical directions respectively. If the range of the projectile is twice the maximum height reached by it,then

$A$ body is thrown horizontally from the top of a tower of height $5 \, m$. It touches the ground at a distance of $10 \, m$ from the foot of the tower. The initial velocity of the body is ......... $m/s$ $(g = 10 \, m/s^2)$.

$A$ particle of mass $m$ is thrown with an initial speed $u$ at an angle $\theta$ with the horizontal. Find the torque of its weight about the point of projection when it reaches the highest point.