$A$ ball is thrown vertically upwards with a velocity $u$. Calculate the velocity with which it falls to the earth again.

Two stones $A$ and $B$ are dropped from a multi-storey building. Stone $A$ is dropped from $100 \, m$ and at the same time stone $B$ is dropped from $50 \, m$ height. Both of them reach the earth at the same time. Will they have equal velocity while reaching the ground? Calculate and find out the answer (Take $g = 10 \, m s^{-2}$).

$A$ ball is dropped from a height of $20\, m$. $A$ second ball is thrown downwards from the same height after one second with initial velocity $u$. If both the balls reach the ground at the same time, calculate the initial velocity of the second ball. (Take $g = 10\, m s^{-2}$).

The atmosphere is held to the earth by

Consider Earth to be a homogeneous sphere. Scientist $A$ goes deep down in a mine and scientist $B$ goes high up in a balloon. The acceleration due to gravity as measured by:

$A$ stone is dropped from the top of a tower. Its speed after it has fallen $20 \, m$ is (Take $g = 10 \, m s^{-2}$): (in $, m s^{-1}$)