From a tower of height $H$, a particle is thrown vertically upwards with a speed $u$. The time taken by the particle to hit the ground is $n$ times that taken by it to reach the highest point of its path. The relation between $H, u$ and $n$ is:

$A$ particle is projected upwards. The times corresponding to height $h$ while ascending and while descending are $t_1$ and $t_2$ respectively. The velocity of projection will be

Find the speed of a body at the ground when it falls freely from a height of $2\,m$. $(g = 10\,ms^{-2})$

$A$ ball is dropped and its displacement versus time graph is as shown (Displacement $x$ from ground and all quantities are positive upwards).
$(a)$ Plot qualitatively velocity versus time graph.
$(b)$ Plot qualitatively acceleration versus time graph.

$A$ man is standing on top of a building $100\, m$ high. He throws two balls vertically,one at $t = 0$ and the other after a time interval $\Delta t$ (less than $2\, s$). The second ball is thrown at a velocity half that of the first. The vertical gap between the first and second ball is $15\, m$ at $t = 2\, s$. The gap is found to remain constant. Calculate the velocity with which the balls were thrown and the exact time interval between their throws.

$A$ stone falls from a balloon that is descending at a uniform rate of $12 \, m/s$. The displacement of the stone from the point of release after $10 \, s$ is.......$m$ $(g = 9.8 \, m/s^2)$