$A$ ball is thrown vertically upwards from the ground $G$ with a speed $u$. It reaches a point $B$ at a height $h$ (lower than the maximum height) after time $t_1$. It returns to the ground after time $t_2$ from the instant it was at $B$ during the upward journey. Then $t_1t_2$ is equal to

$A$ juggler throws balls vertically upwards with the same initial velocity in the air. When the first ball reaches its highest position,he throws the next ball. Assuming the juggler throws $n$ balls per second,the maximum height the balls can reach is

Write the equation of velocity of an object falling freely from height $h$.

Two stones are thrown up simultaneously from the edge of a cliff $200 \; m$ high with initial speeds of $15 \; m s^{-1}$ and $30 \; m s^{-1}$. Verify that the graph shown in Figure correctly represents the time variation of the relative position of the second stone with respect to the first. Neglect air resistance and assume that the stones do not rebound after hitting the ground. Take $g = 10 \; m s^{-2}$. Give the equations for the linear and curved parts of the plot.

$A$ body falls from a large height. The ratio of distance traveled in each time interval $t_0$ during $t = 0$ to $t = 3\, t_0$ of the journey is

$A$ body is projected vertically upwards at time $t=0$ and it is seen at a height $H$ at times $t_1$ and $t_2$ seconds during its flight. The maximum height attained is ($g$ is acceleration due to gravity).