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

From the top of a tower $19.6 \,m$ high, a ball is thrown horizontally. If the line joining the point of projection to the point where it hits the ground makes an angle of $45^{\circ}$ with the horizontal, then the initial velocity of the ball is (in $\,m/s$)

An object is thrown along a direction inclined at an angle of $45^\circ$ with the horizontal direction. The horizontal range of the particle is equal to

$A$ ball is projected with velocity $V_0$ at an angle of elevation $30^o$. Mark the correct statement.

$A$ missile is fired for maximum range at your town from a place $100 \, km$ away from you. If the missile is first detected at its half-way point,how much warning time will you have? (Take $g = 10 \, m/s^2$). What was the speed of the missile when it was detected?

$A$ body is projected with a speed $u$ at an angle $\theta$ with the horizontal. The radius of curvature of the trajectory,when it makes an angle $\left(\frac{\theta}{2}\right)$ with the horizontal is ($g$ = acceleration due to gravity).