Projectile Motion
Understanding motion in two dimensions under constant acceleration due to gravity.
Key Concepts
When an object is launched into the air, it follows a curved path called a trajectory. The only acceleration is gravity acting downward, which creates the characteristic parabolic path.
Independence of Motion
The horizontal and vertical motions are independent:
- Horizontal: Constant velocity (no acceleration)
- Vertical: Constant acceleration due to gravity (g = 9.8 m/s²)
Essential Formulas
Velocity Components
vₓ = v₀ cos θ
vᵧ₀ = v₀ sin θ
Time of Flight
T = 2vᵧ₀ / g = 2v₀ sin θ / g
(when launching and landing at same height)
Maximum Height
H = vᵧ₀² / (2g) = v₀² sin² θ / (2g)
Range (Horizontal Distance)
R = vₓ · T = v₀² sin(2θ) / g
Maximum range at θ = 45°
Key Insights
45° for Maximum Range
When launching from and landing at the same height, a 45° angle gives the maximum horizontal distance.
Time Depends Only on Vertical
The time of flight depends only on the initial vertical velocity, not on the horizontal component.
Symmetric Trajectory
Without air resistance, the path is a perfect parabola. Time going up equals time coming down.
Ready to Practice?
Test your understanding with randomized kinematics problems.
Start Practicing →Interactive Demo
Experiment with different launch angles and speeds to see how they affect the trajectory. Try to achieve maximum range!