During the apex of vertical projectile motion, what is the vertical velocity v_y?

• A. v_y = v0y + g t
• B. v_y = -g t
• C. v_y = g t
• D. v_y = 0

Answer: (D)

At the highest point, the vertical component of motion has stopped for an instant—the direction of the vertical motion is about to reverse from up to down. That moment means the vertical velocity is zero, because the object is not moving upward or downward in the vertical direction at that instant. Gravity is always pulling downward, so right after this moment the vertical velocity becomes negative (downward), while any horizontal velocity (if present) stays the same. If you write vy = vy0 + a_y t, vy reaches zero at the apex after a time t = vy0 / g, which is exactly the instant of the turnaround. So the vertical velocity at the apex is zero.