Mar 20, 2017

We need to consider acceleration of gravity and negligible influence of air.

#### Explanation:

Take two identical projectile and simply drop the first one while you kick the second one from the same initial point.

Both of them will "feel" the only acceleration present, the acceleration of gravity $g = 9.8 \frac{m}{s} ^ 2$ directed downward.
So, even if the second has a horizontal initial velocity this horizontal velocity will not change (no acceleration horizontally) but if you consider the VERTICAL motion they both are going to fall in the same way....both their VERTICAL initial velocities will be zero and will increase at the same rate, for both of them the height $h$ is the same so they will reach the ground at the same time!

You can also throw the second projectile to describe a parabola; if now you throw vertically the first (at the same time) they will againland at the same time!