   Chapter 3, Problem 1CQ

Chapter
Section
Textbook Problem

As a projectile moves in its path, is there any point along the path where the velocity and acceleration vectors are (a) perpendicular to each other? (b) Parallel to each other?

(a)

To determine
If there is any point in a projectile path where the velocity and acceleration vectors are perpendicular to each other.

Yes, at the peak of the path, the velocity and acceleration vectors are perpendicular to each other.

Explanation

The direction of velocity along the path of a projectile is always tangential to the path. The acceleration in a projectile motion is always directed downwards.

Conclusion:

At the peak of the path, the velocity is horizontal, and the acceleration is vertical. Thus, at the peak of the path, the velocity vector is perpendicular to the acceleration vector.

(b)

To determine
If there is any point in a projectile path where the velocity and acceleration vectors are parallel to each other.

No, the velocity and acceleration vectors are can never be parallel to each other.

Explanation

There are two components of the velocity: one is horizontal, and one is vertical. The horizontal component of the velocity always has the same value all over the motion.

Conclusion:

The horizontal velocity remains equal to the initial velocity throughout the motion. For the velocity vector and the acceleration vector to be parallel, the horizontal component of the velocity must he zero, which is not possible.

Thus, the velocity and acceleration can never be parallel in the path of a projectile.

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