$A$ person can jump higher on the surface of the Moon than on the Earth. Why?

$A$ 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 $g = 10\, m s^{-2}$).

Earth is continuously pulling the moon towards its centre,still it does not fall to the earth,why?

$A$ boy on a cliff $49\, m$ high drops a stone. One second later,he throws a second stone after the first. They both hit the ground at the same time. With what speed did he throw the second stone?

$(i)$ How is the force of attraction dependent on the masses of objects and the distance between them?
$(ii)$ The mass of the Earth is $6 \times 10^{24} \, kg$ and that of a natural satellite is $6.5 \times 10^{20} \, kg$. If the distance between them is $3.35 \times 10^{6} \, km$, calculate the force exerted by the Earth on it. $(G = 6.7 \times 10^{-11} \, Nm^{2} kg^{-2})$

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