The following formulae can be used along with the resolution of vectors, and vector addition, to solve problems involving projectiles.
$$ d=\overline{\vphantom{}v}t $$
$$ s=\overline{\vphantom{}v}t $$
$$ v=u+at $$
$$ s=ut+\dfrac{1}{2}at^2 $$
$$ v^2=u^2+2as $$
$$ s=\dfrac{1}{2}(u+v)t $$
The horizontal motion and the vertical motion of a projectile are independent of each other.
Like any vector, the initial velocity of a projectile can be resolved into horizontal and vertical components to use in further calculations on that projectile, as these two quantities are independent of each other.
Satellites are projectiles that are in free fall around a planet/star.
The following is the experiment to measure the acceleration of a falling object.
Apparatus