$A$ balloon starts rising from the ground from rest with an upward acceleration of $2 \, m/s^2$. Just after $1 \, s$,a stone is dropped from it. The time taken by the stone to strike the ground is nearly ....... $s$.

An object is projected upwards from the foot of a tower. The object crosses the top of the tower twice with an interval of $8 \ s$ and the object reaches the foot again after $16 \ s$. The height of the tower is [ $g = 10 \ m/s^2$ ]. (in $m$)

$A$ player throws a ball upwards with an initial speed of $29.4\; m s^{-1}$. Choose the $x=0\; m$ and $t=0\; s$ to be the location and time of the ball at its highest point. Let the vertically downward direction be the positive direction of the $x$-axis. Determine the signs of position,velocity,and acceleration of the ball during its upward and downward motion.

Water drops fall from a tap onto the floor,$5 \ m$ below,at regular intervals of time. The first drop strikes the floor when the sixth drop begins to fall. The height at which the fourth drop will be from the ground at the instant when the first drop strikes the ground is . . . . . . $m$. $(g = 10 \ m/s^2)$

Two bodies $A$ (of mass $1\,kg$) and $B$ (of mass $3\,kg$) are dropped from heights of $16\,m$ and $25\,m$ respectively. The ratio of the time taken by them to reach the ground is:

$A$ ball is dropped from rest at time $t=0$ from a certain height. $A$ second ball is dropped from the same height at time $t=1 \,s$. At what time $t$, does the distance between the two balls become $10 \,m$ (in $s$)?