During the ideal motion of a projectile fired from the Earth surface, which component of its velocity remains constant?

Introduction / Context:
Projectile motion is a standard topic in introductory mechanics. A projectile launched into the air under the influence of gravity follows a curved path, and its velocity changes with time. Understanding which components change and which remain constant is essential for solving many problems. This question reinforces the idea that gravity acts vertically, leaving horizontal motion unaffected when air resistance is neglected.

Given Data / Assumptions:

• The projectile is fired from the Earth surface with an initial velocity at some angle to the horizontal.
• Only the gravitational force acts on the projectile after it is launched.
• Air resistance and other forces are neglected in the ideal model.
• The gravitational acceleration is directed vertically downward and is approximately constant near the surface.
• We are interested in how the velocity components behave during the flight.

Concept / Approach:
In the ideal projectile motion model, gravity is the only force and it acts vertically downward. This produces a constant vertical acceleration and changes the vertical component of velocity over time. There is no horizontal force in this simplified model, so the horizontal acceleration is zero. With zero horizontal acceleration, the horizontal component of velocity remains constant while the vertical component decreases on the way up, becomes zero at the top, and increases downward in magnitude during descent. Total kinetic energy and total momentum both change due to the changing speed and direction.

Step-by-Step Solution:
Step 1: Resolve the initial velocity of the projectile into horizontal and vertical components.Step 2: Note that gravity provides a constant vertical acceleration g downward, which changes the vertical component of velocity with time.Step 3: Recognise that there is no horizontal force in the idealised model, so horizontal acceleration is zero.Step 4: Conclude that the horizontal component of velocity remains constant throughout the flight, while the vertical component varies.

Verification / Alternative check:
Equations of motion confirm this reasoning. Horizontally, x velocity remains equal to its initial value, since acceleration is zero. Vertically, the velocity follows v = u minus g multiplied by t, reflecting constant gravitational acceleration. The magnitude and direction of the total velocity change, so kinetic energy and total momentum also change. Observed projectile paths, such as the flight of a ball, match the predicted parabolic trajectory produced by constant horizontal speed and changing vertical speed.

Why Other Options Are Wrong:
Option a is wrong because kinetic energy depends on the square of speed, and speed changes as the vertical velocity component changes, so energy is not constant. Option b is incorrect because the vector momentum changes in both magnitude and direction as the velocity changes. Option c is wrong since the vertical component clearly changes due to gravity. Option e is also incorrect because only the horizontal component remains constant; the vertical component does not.

Common Pitfalls:
Students sometimes mistakenly believe that if no force acts in the horizontal direction, then the horizontal velocity must also gradually decrease, confusing this with real life situations where air resistance acts. Another common error is to think that total energy must remain constant as kinetic energy, ignoring the fact that potential energy also changes. In projectile motion problems, always separate horizontal and vertical motions, identify where forces act, and then apply the correct constant acceleration equations to each component.

Final Answer:
The horizontal component of its velocity remains constant in the absence of air resistance.