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 $\,m/s$)

$A$ particle is projected at an angle of $30^{\circ}$ from the horizontal at a speed of $60 \; m/s$. The height traversed by the particle in the first second is $h_0$ and the height traversed in the last second before it reaches the maximum height is $h_1$. The ratio $h_0 : h_1$ is . . . . . . . [Take $g = 10 \; m/s^2$]

The maximum range of a gun on a horizontal plane is $16 \,km$. If $g=10 \,ms^{-2}$,then the muzzle velocity of a shell is

$A$ particle is projected with velocity $2 \sqrt{gh}$ at an angle $60^{\circ}$ to the horizontal so that it just clears two walls of equal height $h$ which are at a distance $2h$ from each other. The time taken by the particle to travel between these two walls is

$A$ projectile is thrown in the upward direction making an angle of $60^{\circ}$ with the horizontal direction with a velocity of $150\, ms^{-1}$. Then the time after which its inclination with the horizontal is $45^{\circ}$ is

Two balls are projected with the same velocity but with different angles with the horizontal. Their ranges are equal. If the angle of projection of one is $30^{\circ}$ and its maximum height is $h$,then the maximum height of the other will be