# Projectile Motion Components of Velocity and Speed

In kinematics, I am told that the vertical velocity at the apex of projectile motion is 0. There is still a constant horizontal velocity. Given this, are we not allowed to generalize and say that at the apex, the velocity is 0?

In addition, the speed will never be 0 at the apex because the horizontal velocity is non-zero, right?

• The speed can be 0 if the horizontal velocity is 0. That is, if the projectile is moving straight up, the vertical and horizontal velocity will be 0 at the apex. – JohnHoltz Jun 3 '19 at 1:33

I will use Cartesian coordinates. Assuming you are talking about 2D projectiles, your velocity will be given as:

$$\textbf{v}(t) = \dot{x}_{initial} \hat{x} + (\dot{y}_{initial} - gt)\hat{y}$$

What happens at the apex is that $$t=\frac{\dot{y}_{initial}}{g}$$, so that the y-component of the velocity vanishes as that instant. Evidently, the x-component of the velocity does not depend on time, and hence can only be zero if it is initially zero. Thus, the velocity will be zero at the apex iff the x-component of the velocity is initially zero.