$A$ body dropped from the top of a tower falls through $40 \; m$ during the last two seconds of its fall. The height of the tower is ..... $m$.

Suggest a suitable physical situation for the following $v-t$ graph.

$A$ ball is projected vertically upward with an initial velocity of $50 \; ms^{-1}$ at $t = 0 \; s$. At $t = 2 \; s$,another ball is projected vertically upward with the same velocity. At $t = \dots \; s$,the second ball will meet the first ball $(g = 10 \; ms^{-2})$.

$A$ ball is thrown up vertically with a certain velocity so that it reaches a maximum height $h$. Find the ratio of the times at which it is at height $\frac{h}{3}$ while going up and coming down respectively.

When a ball is dropped into a lake from a height $4.9 \, m$ above the water level,it hits the water with a velocity $v$ and then sinks to the bottom with the constant velocity $v$. It reaches the bottom of the lake $4.0 \, s$ after it is dropped. The approximate depth of the lake is ............ $m$.

$A$ body dropped from the top of a tower covers a distance $7x$ in the last second of its journey,where $x$ is the distance covered in the first second. How much time does it take to reach the ground?