Projectile motion basics (no air resistance) A ball is thrown upward and follows a parabolic trajectory before returning to the ground. Which kinematic quantity remains constant during the entire flight?

Introduction / Context:
Ideal projectile motion (neglecting air resistance) is a cornerstone of engineering mechanics and physics. The motion decomposes into independent horizontal and vertical components. Understanding which quantities remain constant is essential for solving range, time-of-flight, and maximum-height problems quickly and accurately.

Given Data / Assumptions:

• No air resistance; only gravity acts vertically downward.
• Constant gravitational acceleration g acts all along the flight.
• Initial velocity has horizontal and vertical components.

Concept / Approach:
Gravity acts only in the vertical direction, so it does not influence horizontal motion directly. Therefore, in the absence of air drag, the horizontal acceleration is zero. With zero horizontal acceleration, the horizontal component of velocity remains constant throughout the motion. Vertical velocity changes linearly with time due to constant g.

Step-by-Step Solution:

Verification / Alternative check:
At the highest point, the vertical component is momentarily zero while the horizontal component is unchanged since launch (ignoring drag). Both before and after the peak, v_x remains equal to u_x.

Why Other Options Are Wrong:

• Vertical component: Changes linearly with time under gravity.
• Speed: Varies because v_y changes.
• Kinetic energy: Changes with speed, hence not constant.
• None of these: Incorrect since the horizontal component does remain constant.

Common Pitfalls:
Assuming speed is constant because the trajectory is smooth; forgetting to decompose motion; mixing effects of air resistance (not considered here) with the ideal model.

Final Answer:
Horizontal component of velocity