What is the path followed by a projectile under the influence of gravity alone?*1 pointA . ParabolaB . CircleC . Straight lineD . Ellipse

Break Down the Problem

1. Identify the nature of the motion of a projectile under gravity.
2. Assess the options provided to determine which best describes that motion.

Relevant Concepts

• A projectile is any object that is thrown into the air with an initial velocity and is subject only to the force of gravity.
• The path followed by a projectile in a uniform gravitational field is known as a parabolic trajectory.

Analysis and Detail

1. The motion can be decomposed into horizontal (constant velocity) and vertical (accelerated motion due to gravity) components.

2. The horizontal motion does not affect the vertical motion:

   • Horizontal: $x = v_{0x} t$
   • Vertical: $y = h + v_{0y} t - \frac{1}{2}gt^2$ where $g$ is the acceleration due to gravity.

3. Combining these components leads to a parabolic path when plotted on a graph.

Verify and Summarize

• The analysis confirms that under the influence of gravity alone, without air resistance, the trajectory of a projectile is indeed parabolic.

Final Answer

A. Parabola