Physics
Projectile Motion
Projectile motion is 2D motion under gravity alone. Horizontal velocity stays constant; vertical motion is uniformly accelerated. Decompose the launch into x and y components and the rest is kinematics.
How to Approach Projectile Motion
- 01
Decompose the initial velocity
v₀ₓ = v₀·cos(θ), v₀ᵧ = v₀·sin(θ). The angle θ is measured from horizontal.
- 02
Apply kinematics to each axis
Horizontal: x = v₀ₓ·t (no acceleration). Vertical: y = v₀ᵧ·t - ½g·t² (acceleration -g, downward).
- 03
Solve for the unknown
Range, max height, and time-of-flight have closed-form expressions. Range = v₀²·sin(2θ)/g. Max height = (v₀·sin θ)²/(2g). Time-of-flight = 2v₀·sin(θ)/g.
Frequently Asked Questions
What angle gives maximum range?
45° — but only if the launch and landing heights are equal. From a height above the ground, the optimal angle is slightly less than 45°.
Does horizontal velocity affect time-of-flight?
No — time-of-flight depends only on the vertical motion. A bullet fired horizontally hits the ground at the same time as a bullet dropped from the same height.
How does air resistance change things?
It shortens range and lowers max height. For most intro physics problems, air resistance is ignored unless explicitly mentioned.
Related Topics
More step-by-step guides in Physics and adjacent subjects.
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