Q3DQ - University Physics with Modern Physics

Question

A projectile moves in a parabolic path without air resistance. Is there any point at which $\overrightarrow{\mathbf{a}}$ is parallel to $\overrightarrow{\mathbf{v}}$? Perpendicular to $\overrightarrow{\mathbf{v}}$? Explain

Step-by-Step Solution

Answer

The acceleration $\overrightarrow{a}$ will never parallel to $\overrightarrow{v}$ and perpendicular to the flight's highest point. 

Step 1: Concept/Significance of projectile motion.

Projectile motion is the movement of a projectile. The motion of a body under the only action of gravity is taught in general under this topic (vertically downwards).

Step 2: Determination of point at which a → is parallel to v → .

The path of a projectile is a parabola in the given by,

The acceleration $\overrightarrow{a}$ will never be parallel to $\overrightarrow{v}$, and it will always be perpendicular to $\overrightarrow{v}$ at the maximum height. Because an is the downward acceleration caused by gravity, it will never be parallel to v. At no time does the projectile's velocity point down.

 

Thus, the acceleration $\overrightarrow{a}$ will never parallel to $\overrightarrow{v}$ and perpendicular to the flight's highest point.