How does the horizontal velocity of a projectile change during its flight in a vacuum?

The horizontal velocity remains constant throughout the flight. This is because there are no horizontal forces acting on the object, resulting in zero horizontal acceleration ($a_x = 0$).

What is the difference between the total velocity and the vertical velocity at the peak of a projectile's path?

At the peak, the vertical velocity ($v_y$) is exactly zero. However, the total velocity is not zero; it is equal to the constant horizontal velocity ($v_x$) at that point.

Why do two projectiles launched at $30^{\circ}$ and $60^{\circ}$ with the same speed land at the same horizontal distance?

These are complementary angles (sum to $90^{\circ}$). While the $60^{\circ}$ launch stays in the air longer, the $30^{\circ}$ launch has a higher horizontal velocity, and these factors mathematically balance out to produce the same range.

What common error occurs when calculating the time of flight using the total initial velocity $v_0$?

Using $v_0$ instead of the vertical component $v_{0y}$ is a mistake because gravity only affects the vertical motion. Time of flight is determined strictly by vertical parameters ($v_{0y}$, $g$, and height).

What happens to the calculation if the downward direction is not consistently defined as negative?

Inconsistent sign conventions lead to incorrect time or displacement values. If 'up' is positive, gravity ($g$) must be negative; if 'down' is positive, the initial upward velocity must be negative.

Define 'Trajectory' in the context of projectile motion.

A trajectory is the specific curved path that an object follows through space as a function of time. In projectile motion without air resistance, this path is always a parabola.

What is the 'Range' of a projectile?

The range is the total horizontal distance traveled by the projectile from its starting point to the point where it returns to its original launch height.

How does the mass of a projectile affect its range in a vacuum?

Mass has no effect on the range, height, or time of flight. According to the equivalence principle, all objects in a vacuum experience the same gravitational acceleration regardless of their mass.

When should you use the equation $x = v_x t$ versus $y = v_{0y}t - \frac{1}{2}gt^2$?

Use $x = v_x t$ for horizontal displacement where velocity is constant. Use the quadratic $y$ equation for vertical displacement where acceleration is constant due to gravity.

What is the vertical acceleration of a projectile at the very top of its path?

The vertical acceleration is still $g$ (approx $9.8 \text{ m/s}^2$) downward. A common misconception is that acceleration is zero at the peak because velocity is zero, but gravity never stops acting on the object.

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AS-Level

Cambridge International Examinations

Physics

2. Kinematics

Projectile Motion

Summary

Projectile motion is a form of two-dimensional kinematics where an object moves in a curved path under the sole influence of gravity. The core insight of this topic is the independence of horizontal and vertical components, allowing complex motion to be analyzed as two simultaneous linear motions.

1. Definition & Core Concepts

Projectile Motion refers to the motion of an object (the projectile) that is launched into the air and moves along a curved path called a trajectory under the influence of gravity alone.
The fundamental principle is the independence of motion, which states that the horizontal and vertical components of the motion do not affect each other and can be solved separately.
In an ideal model, we assume no air resistance, meaning the only force acting on the object after launch is the downward pull of gravity, resulting in a constant vertical acceleration.
The resulting path of any projectile in a uniform gravitational field without air resistance is always a parabola.

A diagram showing a parabolic trajectory of a projectile with initial velocity vector v0, constant horizontal velocity vx at the peak, and downward acceleration g.

2. Underlying Principles

3. Methods & Techniques

4. Key Distinctions

5. Exam Strategy & Tips

6. Common Pitfalls & Misconceptions