$A$ ball is thrown up and attains a maximum height of $100 \, m$. It is thrown upwards with a speed of: (in $, m/s$)

The acceleration due to gravity at the moon's surface is $1.67 \, m s^{-2}$. If the radius of the moon is $1.74 \times 10^{6} \, m$,calculate the mass of the moon. (Use $G = 6.67 \times 10^{-11} \, N m^{2} kg^{-2}$)

$A$ soft drink bottle is dropped by a waiter from the top of a hotel whose height is $100 \, m$. It takes $T$ seconds to reach the ground. Where will it be at $T/2$ seconds?

At what point in its trajectory does a projectile have its $(i)$ maximum speed and $(ii)$ minimum speed?

Show that the weight of an object on the moon is one-sixth of its weight on the earth. [Given: mass of earth $= 5.98 \times 10^{24} \ kg$,mass of moon $= 7.36 \times 10^{22} \ kg$,radius of earth $= 6.37 \times 10^{6} \ m$,radius of moon $= 1.74 \times 10^{6} \ m$]

The Earth is acted upon by the gravitation of the Sun,even though it does not fall into the Sun. Why?