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
Decompose the initial velocity
v₀ₓ = v₀·cos(θ), v₀ᵧ = v₀·sin(θ). The angle θ is measured from horizontal.
Apply kinematics to each axis
Horizontal: x = v₀ₓ·t (no acceleration). Vertical: y = v₀ᵧ·t - ½g·t² (acceleration -g, downward).
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.
Stuck on a Projectile Motion problem?
Snap a photo or type the question. ScanSolve walks you through every step — same as the worked examples above. 5 free solves per day, no card required.