Projectile motion tips: breaking down A-level physics problems

Projectile motion is a classic A-level physics topic that trips up even strong students. The combination of horizontal and vertical motion, plus projectile motion equations, can seem overwhelming. Here’s how I break it down in my tutoring sessions.

The Core Concept

A projectile is anything moving under the influence of gravity alone (ignoring air resistance). The key insight? Horizontal and vertical motion are independent.

This means:

• Horizontal velocity stays constant
• Vertical velocity changes due to gravity
• You can treat them separately!

My 5-Step Approach

Step 1: List What You Know

Before diving into equations, make a clear table:

The tip: “What are you trying to find?” should be your first question. This prevents you from using the wrong equations.

Step 2: Resolve Initial Velocity

This is where many students stumble. If a ball is kicked at 15 m/s at 30° to the horizontal, you need:

Common mistake: Using the wrong angle or forgetting to convert to m/s.

Step 3: Identify Which Motion is Simpler

Typically, horizontal motion is simpler - just s = vt because there’s no acceleration.

My heuristic: If the problem asks “how far?” or “how long?”, start with horizontal if you know the time, or vertical if you need to find the time.

Step 4: The Time Connector

Time is the same for both motions! Once you know it from one direction, use it for the other.

Step 5: Question-Specific Strategies

Finding maximum height: Use v² = u² + 2as in the vertical direction with v = 0 at the top.

Finding range: Find time of flight (when s_y = 0), then use that time with horizontal motion.

Finding velocity at a point: Find horizontal and vertical velocities separately, then use Pythagoras for the magnitude.

Real Example: Football Kick Problem

From a recent session with a student named James

Problem: A football is kicked with an initial velocity of 20 m/s at 35° to the horizontal. Find: a) The maximum height b) The time of flight c) The range

Our working:

Part (a) - Maximum height

At max height, $v_y = 0$. Using $v^2 = u^2 + 2as$:

Part (b) - Time of flight

When it lands, $s_y = 0$. Using $s = ut + \frac{1}{2}at^2$:

Therefore: $t = 0$ (start) or $t = 2.35$ s (landing)

Time of flight = 2.35 s

Part (c) - Range

Common Pitfalls I See

1. Forgetting the minus sign on gravitational acceleration - it’s $-9.8$ m/s², not $+9.8$!

2. Not completing the calculation - finding the projectile equation but forgetting to substitute the time back in.

3. Angle confusion - make sure you’re using the angle to the horizontal, not the vertical.

4. Mixing up displacement and distance - these are different! Displacement can be negative.

The Pattern Recognition

After doing enough of these problems, you’ll notice patterns:

• Maximum height is always $\frac{u_y^2}{2g}$
• Time of flight is always $\frac{2u_y}{g}$
• Range is always $\frac{u^2 \sin(2\theta)}{g}$ for level ground

But don’t just memorize these - understand WHY they work!

When to Use SUVAT vs Projectile Equations

SUVAT: Use when you have specific points to analyze

• “Find velocity after 2 seconds”
• “How far does it go in 3 seconds?”

Projectile equations: Use when you need the general trajectory

• “Find the equation of the path”
• “Prove this is a parabola”

Often, you’ll use SUVAT to find specific values, then use those in projectile equations.

The “Aha Moment”

The biggest breakthrough comes when students realize that “straight up and down” is just a special case of projectile motion where $u_x = 0$. All the same principles apply!

Next Steps

Start with simple problems (level ground, no obstacles) before moving to more complex scenarios. Practice resolving velocities until it’s second nature - this skill carries over to circular motion, forces, and beyond!