Two balls are dropped from heights $h$ and $2h$ respectively from the Earth's surface. The ratio of the time taken by these balls to reach the Earth is

$A$ stone is dropped from a height of $100 \ m$, while another one is projected vertically upwards from the ground with a velocity of $25 \ m/s$ at the same time. The time in seconds after which they will have the same height is (acceleration due to gravity, $g = 10 \ m/s^2$):

$A$ body is thrown vertically upwards with velocity $u$. The distance travelled by it in the fifth and the sixth seconds are equal. The velocity $u$ is given by.........$m/s$ $(g = 9.8\, m/s^{2})$

What is the initial velocity of an object falling freely (in $m/s$)?

$A$ ball is dropped from a height of $90 \; m$ on a floor. At each collision with the floor,the ball loses one-tenth of its speed. Plot the speed-time graph of its motion between $t = 0$ to $12 \; s$.

$A$ ball is thrown upward with an initial velocity $V_0$ from the surface of the earth. The motion of the ball is affected by a drag force equal to $m\gamma v^2$ (where $m$ is the mass of the ball,$v$ is its instantaneous velocity,and $\gamma$ is a constant). The time taken by the ball to rise to its zenith is: