Lesson 7: Kinematics & Projectile Motion
Kinematics describes motion without asking about its cause. When an object moves under gravity alone (ignoring air resistance), it follows a parabolic path — this is projectile motion, and it can be analyzed by splitting the motion into independent horizontal and vertical components.
Key Concepts
Key Equations
v = v₀ + at | x = v₀t + ½at² | v² = v₀² + 2ax. For projectiles: horizontal velocity is constant (aₓ=0). Vertical acceleration = −9.8 m/s² (gravity down).
Component Analysis
Any velocity at an angle θ splits into: vₓ = v·cos θ (horizontal) and vᵧ = v·sin θ (vertical). These components are independent — they don't affect each other.
Time of Flight
Determined entirely by vertical motion. The projectile rises until vᵧ = 0, then falls. Total flight time = 2·(v·sin θ)/g for level ground launch.
Horizontal Range
R = v₀²·sin(2θ)/g. Maximum range occurs at θ = 45°. Angles that are supplementary (e.g., 30° and 60°) give equal range.
Real-World Applications
Ballistics, sports (basketball, soccer), fluid jets, ramps — all use projectile motion principles. In the real world, air resistance modifies the ideal parabola.
🔬 Virtual Lab: Projectile Motion Simulator
Set launch angle and speed, then fire. Watch the parabolic trajectory animate in real time. Read off the max height and range.
✅ Check Your Understanding
1. At what angle does a projectile achieve maximum horizontal range (ignoring air resistance)?
2. Which component of velocity changes during projectile flight?
3. A ball launched at 60° and one launched at 30° at the same speed will: