What is the acceleration due to gravity at the centre of the earth (in $m/s^2$)?

What is the name given to the path followed by a projectile?

$A$ man at the top of a tower throws an object horizontally,whereas he simply drops another. Will these two objects reach the earth at the same time?

$A$ stone is dropped from the edge of a roof.
$(a)$ How long does it take to fall $4.9 \, m$?
$(b)$ How fast does it move at the end of that fall?
$(c)$ How fast does it move at the end of $7.9 \, m$?
$(d)$ What is its acceleration after $1 \, s$ and after $2 \, s$?

$A$ bomb is released from an aircraft. Its trajectory is:

If your weight on the Earth is $450 N$,calculate your weight on planet Mars. (Radius of Mars $= 4.3 \times 10^{6} m$,mass of Mars $= 6 \times 10^{23} kg$ and gravitational constant $G = 6.67 \times 10^{-11} Nm^{2} kg^{-2}$). Take acceleration due to gravity on Earth as $10 m s^{-2}$.