Question

For a projectile motion, the angle between the velocity and acceleration is minimum and acute at

• A. Only one point
• B. Two points
• C. Three points
• D. Four points

Answer 1

The Correct Option is A

1. Understanding Projectile motion

In projectile motion, the acceleration is constant and directed downwards due to gravity.
Velocity changes in both magnitude and direction throughout the trajectory.
The angle between two vectors is minimum when they are in the same direction (or as close as possible).

2. Analyzing the Trajectory:

• At the initial point, the angle between velocity and acceleration will be obtuse because the initial velocity has an upward component while the acceleration is downward.
• At the highest point of the trajectory, the vertical component of velocity is zero, and the velocity is purely horizontal. The acceleration, due to gravity, is still acting downwards. Therefore, the angle between velocity and acceleration is exactly 90 degrees.
• Throughout the path, except at the highest point, the angle between the velocity and acceleration vectors is acute, but there is only one point where the angle is both minimum and acute.

3. Minimum and Acute:

At the beginning of the trajectory, the angle is large (greater than 90 degrees).
As the projectile moves towards the highest point, the angle decreases and becomes 90 degrees at the highest point.
After the highest point, the angle decreases further to become an acute angle, and it reaches its minimum value at a single point where the velocity vector is closest to being aligned with the acceleration vector.
Therefore, the angle between velocity and acceleration is both acute and minimum at only one point in the trajectory.

4. Final Answer:

The correct answer is: (A) only one point.

Answer 2

In projectile motion, the center of acceleration is always directed toward the Earth's center. At the peak point of the trajectory, the angle between the velocity and acceleration is 90 degrees because the vertical component of velocity becomes zero. As a result, the velocity is at its minimum and is purely horizontal. This 90-degree angle occurs only at the highest point, making it the sole instance where the angle between velocity and acceleration is exactly perpendicular. At all other points, the angle is acute.

The Correct Answer is (A): Only one point