Suppose I am on the moon. So I am throwing a rock upwards in a velocity of $v$ with an angle of $a$ with the ground. Now we can divide the velocity in two components. One is perpendicular to the ground ($v1$) and another parallel to the ground ($v2$). Now there is gravity of moon, so the rock will gain a maximum height due to $v1$ and after that it will ascend no more.
But as there is no air resistance on moon, so there is no force to resist $v2$. So my question is 'Will the rock reach a height and continue to move parallel to the ground in a velocity of $v2$ or not?' If it won't happen, then why won't it happen?