In projectile motion, is there any point along the trajectory where the velocity vector $\overrightarrow{v}$ and the acceleration vector $\overrightarrow{a}$ are parallel to each other? If so, where does this occur?

• A. Yes, at the moment of launch.
• B. Yes, at the highest point of the trajectory.
• C. Yes, at the point where the projectile lands.
• D. No, they are never parallel during the trajectory.

Answer: (A)

Verified step by step guidance

1. Recall that in projectile motion, the acceleration vector \( \vec{a} \) is constant and points vertically downward due to gravity, with magnitude \( g \). This means \( \vec{a} = -g \hat{j} \), where \( \hat{j} \) is the unit vector in the vertical direction.
2. The velocity vector \( \vec{v} \) changes throughout the motion. It has both horizontal and vertical components: \( \vec{v} = v_x \hat{i} + v_y \hat{j} \), where \( v_x \) is constant and \( v_y \) changes due to gravity.
3. To determine if \( \vec{v} \) and \( \vec{a} \) are parallel, their directions must be the same or exactly opposite. Since \( \vec{a} \) points straight down, \( \vec{v} \) must also point straight down or straight up for them to be parallel.
4. At the highest point of the trajectory, the vertical component of velocity \( v_y = 0 \), so \( \vec{v} \) is purely horizontal and thus perpendicular to \( \vec{a} \). Therefore, they are not parallel there.
5. At the moment of launch and at the point of landing, the velocity vector has both horizontal and vertical components, but only at the moment of launch if the projectile is launched vertically downward or upward will \( \vec{v} \) and \( \vec{a} \) be parallel. In typical projectile motion (launched at an angle), \( \vec{v} \) and \( \vec{a} \) are not parallel except at the moment of launch if the velocity vector is aligned with gravity.